Calculus: The Logical Extension of Arithmetic

Infinity Times Zero and the Concept of Integration

Author(s): Seymour B. Elk

Pp: 186-261 (76)

DOI: 10.2174/9781681082035116010008

* (Excluding Mailing and Handling)

Abstract

In this chapter, the second of the processes in the traditional sequence of courses that comprise the calculus curriculum, “integral calculus”, is examined in terms of its algebraic foundation. A new paradigm is proposed that views “integration”, also often designated as “anti- (or inverse) differentiation”, as a form of infinity multiplied by zero. Such a protocol is demonstrated as being the inverse operation to the previously developed process of differentiation in Chapter 3. However, unlike the function produced by the process of differentiation, this inverse is either not unique and needs to be supplemented with an arbitrary unspecified constant (which is addended to the generated function) or a set of limits. Along with “sloughing through” several of the techniques associated with such anti-differentiation, the mathematical underpinning of this inverse operation is introduced. This is then supplemented by an expansion of the horizon of “what is mathematics?” to introduce (1) a special (more advanced) function, called the Dirac delta function, which, in an altogether different manner is also subsumed by the over-arching concept of infinity multiplied by zero, and (2) the theoretical base from one limited to continuous functions (called “Riemann integration”) to a larger set that includes selected discontinuous functions (called “Lebesgue integration”).


Keywords: Anti-Derivatives, Area of Surface of Revolution, Dirac Delta, Direct Substitutions, Indirect Substitutions, Integral Calculus, Integration By Parts, Kronecker Delta, Lebesque Integral, Length of Planar Curves, Volume of Revolution (Slices vs. Shells).

Related Books
© 2025 Bentham Science Publishers | Privacy Policy
Request history8.2.27PHP Version366msRequest Duration26MBMemory UsageGET chapter/{id}/{param?}Route
  • warninglog[04:57:59] LOG.warning: Optional parameter $id declared before required parameter $request is implic...
  • Booting (148ms)time
  • Application (219ms)time
  • 1 x Application (59.7%)
    219ms
    1 x Booting (40.3%)
    148ms
    12 templates were rendered
    • ebook.chapter_detailschapter_details.blade.php#?blade
    • layouts.chapter_header_sectionchapter_header_section.blade.php#?blade
    • ebook.chapter_top_bannerchapter_top_banner.blade.php#?blade
    • ebook.chapter_bottom_bannerchapter_bottom_banner.blade.php#?blade
    • ebook.ebook_right_bannerebook_right_banner.blade.php#?blade
    • includes.inc_related_journalsinc_related_journals.blade.php#?blade
    • includes.inc_related_ebooksinc_related_ebooks.blade.php#?blade
    • layouts.appapp.blade.php#?blade
    • layouts._login_access_login_access.blade.php#?blade
    • layouts._header_header.blade.php#?blade
    • layouts._main_menu_main_menu.blade.php#?blade
    • layouts._footer_menu_footer_menu.blade.php#?blade
    uri
    GET chapter/{id}/{param?}
    middleware
    web, check_user_access
    controller
    App\Http\Controllers\ChapterController@GetChapterDetails
    namespace
    App\Http\Controllers
    where
    as
    chapter
    file
    app/Http/Controllers/ChapterController.php:1350-1704
    18 statements were executed118ms
    • Connection Establishedalphaeurekaselec_live_10_06_2022UserAccessCheck.php#24
      Backtrace
      • 9. middleware::check_user_access:24
      • 10. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 11. vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
      • 12. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 13. vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:88
    • INSERT INTO visitor_ip_address (ip_address,visitor_agent,visitor_count, created_on,updated_on) VALUES ('59620938','',1,1740459479,1740459479) ON DUPLICATE KEY UPDATE visitor_count=visitor_count + 1, updated_on=1740459479
      13.52msalphaeurekaselec_live_10_06_2022UserAccessCheck.php#24
      Backtrace
      • 11. middleware::check_user_access:24
      • 12. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
      • 14. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 15. vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:88
    • INSERT INTO visitor_ip_address_detail (ip_address,visitor_url,visitor_count, created_on,updated_on) VALUES ('59620938','/chapter/9751',1,1740459479,1740459479)
      250μsalphaeurekaselec_live_10_06_2022UserAccessCheck.php#27
      Backtrace
      • 11. middleware::check_user_access:27
      • 12. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
      • 14. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 15. vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:88
    • (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_journal_volume_trail WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_journal_volume_corporate WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_journal_volume_token WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_ebook_volume_trail WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_ebook_volume_corporate WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_ebook_volume_token WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_issue_trail WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_issue_corporate WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_issue_token WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_article_trail WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_article_corporate WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_article_token WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_chapter_trail WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_chapter_corporate WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_chapter_token WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) union (select `user_id`, `to_ip`, `from_ip` from (select user_id, to_ip, from_ip FROM user_access_disease_corporate WHERE to_ip >= 59620938 ORDER BY to_ip ASC LIMIT 1) as `tjv` where `from_ip` <= 59620938) limit 1
      31.27msalphaeurekaselec_live_10_06_2022UserAccess.php#784
      Bindings
      • 0: 59620938
      • 1: 59620938
      • 2: 59620938
      • 3: 59620938
      • 4: 59620938
      • 5: 59620938
      • 6: 59620938
      • 7: 59620938
      • 8: 59620938
      • 9: 59620938
      • 10: 59620938
      • 11: 59620938
      • 12: 59620938
      • 13: 59620938
      • 14: 59620938
      • 15: 59620938
      Backtrace
      • 14. app/Models/UserAccess/UserAccess.php:784
      • 15. middleware::check_user_access:114
      • 16. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
      • 18. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
    • select * from `chapter` where `chapter_id` = '9751' limit 1
      530μsalphaeurekaselec_live_10_06_2022ChapterController.php#1406
      Bindings
      • 0: 9751
      Backtrace
      • 16. app/Http/Controllers/ChapterController.php:1406
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select CONCAT_WS(' ',au.first_name, ' ', ifnull(au.initials,''), ' ', au.last_name) as authors, CONCAT(au.last_name, IFNULL(CONCAT(' ', au.initials), ''), ' ', au.first_name) AS authorsRIS, CONCAT_WS(' ',au.last_name, ' ', ifnull(au.initials,''), ' ', au.first_name) as authorsCiteAs, CONCAT_WS(' ',au.first_name, IFNULL(CONCAT(' ', au.initials), ''), IFNULL(CONCAT(' ', au.last_name), '')) as authorsmodal , `au`.*, `af`.`ror_id`, `af`.`institution`, `af`.`department`, `af`.`country`, `af`.`city`, `af`.`address`, (GROUP_CONCAT(TRIM(BOTH ', ' FROM CONCAT(ifnull(concat(af.institution,','),''), ifnull(concat(af.department,','),''), ifnull(concat(af.address,','),''), ifnull(concat(af.city,','),''), ifnull(concat(af.country,','),''), ifnull(concat(af.postal_code,','),''), ifnull(concat(af.phone,','),''), ifnull(concat(af.fax,','),''))) SEPARATOR '|')) as `author_affiliation`, (GROUP_CONCAT(TRIM(BOTH ', ' FROM CONCAT(ifnull(concat(af.web_view,','),''))) SEPARATOR '|')) as `web_view` from `author` as `au` left join `author_affiliation` as `af` on `au`.`author_id` = `af`.`author_id` where `au`.`chapter_id` = '9751' group by `au`.`author_id` order by `au`.`article_id` asc, `au`.`sequence` asc
      9.74msalphaeurekaselec_live_10_06_2022Author.php#86
      Bindings
      • 0: 9751
      Backtrace
      • 13. app/Models/Author.php:86
      • 14. app/Http/Controllers/ChapterController.php:1411
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `keywords` where `chapter_id` = '9751'
      33.02msalphaeurekaselec_live_10_06_2022ChapterController.php#1415
      Bindings
      • 0: 9751
      Backtrace
      • 15. app/Http/Controllers/ChapterController.php:1415
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select * from `ebook` where `ebook_id` = 616 limit 1
      430μsalphaeurekaselec_live_10_06_2022ChapterController.php#1430
      Bindings
      • 0: 616
      Backtrace
      • 16. app/Http/Controllers/ChapterController.php:1430
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select count(*) as aggregate from `subject_ebook` as `se` inner join `ebook` as `e` on `e`.`ebook_id` = `se`.`ebook_id` inner join `ebook_volume` as `v` on `v`.`ebook_id` = `e`.`ebook_id` where subject_id IN (select subject_id FROM subject_ebook WHERE ebook_id=616) and se.ebook_id!=616 and v.ebook_status='1'
      1.47msalphaeurekaselec_live_10_06_2022Subject.php#238
      Backtrace
      • 16. app/Models/Subject.php:238
      • 17. app/Http/Controllers/ChapterController.php:1434
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 19. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select distinct v.nid as volume_id,e.nid,e.title,v.issn,v.eissn,v.isbn,v.eisbn,e.ebook_id, v.image_file_name,v.file_path,v.flyer_link,v.ebook_volume_id, v.volume_name,v.doi,v.year_id,v.introduction from `subject_ebook` as `se` inner join `ebook` as `e` on `e`.`ebook_id` = `se`.`ebook_id` inner join `ebook_volume` as `v` on `v`.`ebook_id` = `e`.`ebook_id` where subject_id IN (select subject_id FROM subject_ebook WHERE ebook_id=616) and se.ebook_id!=616 and v.ebook_status='1' limit 10 offset 0
      1.1msalphaeurekaselec_live_10_06_2022Subject.php#238
      Backtrace
      • 14. app/Models/Subject.php:238
      • 15. app/Http/Controllers/ChapterController.php:1434
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as aggregate from `subject_journal` as `sj` inner join `journal` as `j` on `j`.`journal_id` = `sj`.`journal_id` where subject_id IN (select subject_id FROM subject_ebook WHERE ebook_id=616)
      450μsalphaeurekaselec_live_10_06_2022Subject.php#255
      Backtrace
      • 16. app/Models/Subject.php:255
      • 17. app/Http/Controllers/ChapterController.php:1435
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 19. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `e`.*, `a`.*, `y`.`year`, `e`.`ebook_volume_id` as `ebook_volume_id`, `a`.`ebook_volume_id` as `ebk_vol_id`, `e`.`ebook_id` as `ebk_ebook_id` from `ebook_volume` as `e` left join `author` as `a` on `e`.`ebook_volume_id` = `a`.`ebook_volume_id` left join `year` as `y` on `y`.`id` = `e`.`year_id` where `e`.`ebook_volume_id` = 2186 and `e`.`is_uploaded` = 1
      17.94msalphaeurekaselec_live_10_06_2022EbookVolume.php#271
      Bindings
      • 0: 2186
      • 1: 1
      Backtrace
      • 13. app/Models/EbookVolume.php:271
      • 14. app/Http/Controllers/ChapterController.php:1438
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) rcd from `ebook_volume` where `ebook_id` = 616 and ebook_volume_id <> 2186 limit 1
      610μsalphaeurekaselec_live_10_06_2022EbookVolume.php#999
      Bindings
      • 0: 616
      Backtrace
      • 14. app/Models/EbookVolume.php:999
      • 15. app/Http/Controllers/ChapterController.php:1462
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from ebook_access where content_type_id = '9751' and content_type = 'c' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      2.95msalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1465
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from ebook_access where content_type_id = '2186' and content_type = 'v' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      490μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1478
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"ebook_volume" as access_level,"" as chapter_id from `user_access_ebook_volume_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59620938 and j.to_ip >=59620938 )) and ((j.from_date <= 1740459479 and j.to_date >= 1740459479 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 2186) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"ebook_volume" as access_level,"" as chapter_id from `user_access_ebook_volume_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59620938 and j.to_ip >=59620938 )) and ((j.from_date <= 1740459479 and j.to_date >= 1740459479 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 2186) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"ebook_volume" as access_level,"" as chapter_id from `user_access_ebook_volume_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59620938 and j.to_ip >=59620938 )) and ((j.from_date <= 1740459479 and j.to_date >= 1740459479 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 2186)
      1.07msalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59620938 and j.to_ip >=59620938 )) and ((j.from_date <= 1740459479 and j.to_date >= 1740459479 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9751) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59620938 and j.to_ip >=59620938 )) and ((j.from_date <= 1740459479 and j.to_date >= 1740459479 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9751) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59620938 and j.to_ip >=59620938 )) and ((j.from_date <= 1740459479 and j.to_date >= 1740459479 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9751)
      1msalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2186 and `b`.`banner_from_date` <= 1740459479 and `b`.`banner_to_date` >= 1740459479 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.91msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2186
      • 3: 1740459479
      • 4: 1740459479
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='385f979c105eb7f703376339cc2fbec3'
      320μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    11Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        56bxuk0mCZ0nVKqVOrl8FXU7JX2olV7aEIcokfAX
        uc_cart_id
        385f979c105eb7f703376339cc2fbec3
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/9751" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/9751
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6Ino5NVRxcFY4TUM3Q3g1aGwxRkJ5TXc9PSIsInZhbHVlIjoiTEJaUm9CbWc2ZEVmRG9pRUZ3WHh0UFcySXViNDh4TWZoY1B6OVpaLzBUbz0iLCJtYWMiOiJiZDI2MmM4ZDUwMDdlMTJjMGY3YWFmZGEzZjkxYTZlYTY2YTIzNzhkNjg4ZDQ5NTI2MGQ5ZTg1NjI1OTlkZTI2IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6Ino5NVRxcFY4TUM3Q3g1aGwxRkJ5TXc9PSIsInZhbHVlIjoiTEJaUm9CbWc2ZEVmRG9pRUZ3WHh0UFcySXViNDh4TWZoY1B6OVpaLzBUbz0iLCJtYWMiOiJiZDI2MmM4ZDUwMDdl" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 04:57:59 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjdzamRCMUVJMEpYYnc3L250WTB5U0E9PSIsInZhbHVlIjoidDdWZmdpTzlTUFNkU1NNMkRubjU3VEcrdkhGVkpDNllUOW96SS9HdFJoVW8vdno4VVBOSTNVODcremhnVEtFa1VBSEQrN3BQVmpkc003S1RIS2wyb0NQS2d0VjJtc0pTbnl5bU0zN2UrZnNjUTRtZ1BKV05yVEJjUTU0ZGs0RGEiLCJtYWMiOiIzM2JiMjRhMzllODQ1MzUzZjRkNTMzMWI2ZjBhMjY1MWJjZDkyM2ZmN2JkNTQyMDk4OGU4MjhlNmU3MGNiNmZiIiwidGFnIjoiIn0%3D; expires=Thu, 27 Feb 2025 16:57:59 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IjdzamRCMUVJMEpYYnc3L250WTB5U0E9PSIsInZhbHVlIjoidDdWZmdpTzlTUFNkU1NNMkRubjU3VEcrdkhGVkpDNllUOW96SS9HdFJoVW8vdno4VVBOSTNVODcremhnVEtFa1VBSEQrN" 1 => "alphaeurekaselectnet_session=eyJpdiI6IkhIZ3lWMTRlYklyanZZZVlucUNQcWc9PSIsInZhbHVlIjoiMThuUEVOR2E1THJpV2FVSitHQ1hGWkplVGxPbjdhek9qSGlMeVhzcFZycDI3L21oaFROMllyTzBzZGFzTUlIeHhPa2ZJMUNWbzFmNmxpeFBZeTZvL2J4Zmk0QnV6UFRUSXU5bFFPSHVWdER1a1pqbFNNL1Y3dW5YTG5GdHZEeFAiLCJtYWMiOiJhMWNkNTBkYmE2MmMyYmY3NmYyOGQ0YjlmZTVlZjY5YzhhZWFlMDA4YzljMjZlMTc0MDZiYmM1MzkzMzEwNDhiIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6IkhIZ3lWMTRlYklyanZZZVlucUNQcWc9PSIsInZhbHVlIjoiMThuUEVOR2E1THJpV2FVSitHQ1hGWkplVGxPbjdhek9qSGlMeVhzcFZycDI3L21oaFROMllyTzB" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjdzamRCMUVJMEpYYnc3L250WTB5U0E9PSIsInZhbHVlIjoidDdWZmdpTzlTUFNkU1NNMkRubjU3VEcrdkhGVkpDNllUOW96SS9HdFJoVW8vdno4VVBOSTNVODcremhnVEtFa1VBSEQrN3BQVmpkc003S1RIS2wyb0NQS2d0VjJtc0pTbnl5bU0zN2UrZnNjUTRtZ1BKV05yVEJjUTU0ZGs0RGEiLCJtYWMiOiIzM2JiMjRhMzllODQ1MzUzZjRkNTMzMWI2ZjBhMjY1MWJjZDkyM2ZmN2JkNTQyMDk4OGU4MjhlNmU3MGNiNmZiIiwidGFnIjoiIn0%3D; expires=Thu, 27-Feb-2025 16:57:59 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IjdzamRCMUVJMEpYYnc3L250WTB5U0E9PSIsInZhbHVlIjoidDdWZmdpTzlTUFNkU1NNMkRubjU3VEcrdkhGVkpDNllUOW96SS9HdFJoVW8vdno4VVBOSTNVODcremhnVEtFa1VBSEQrN" 1 => "alphaeurekaselectnet_session=eyJpdiI6IkhIZ3lWMTRlYklyanZZZVlucUNQcWc9PSIsInZhbHVlIjoiMThuUEVOR2E1THJpV2FVSitHQ1hGWkplVGxPbjdhek9qSGlMeVhzcFZycDI3L21oaFROMllyTzBzZGFzTUlIeHhPa2ZJMUNWbzFmNmxpeFBZeTZvL2J4Zmk0QnV6UFRUSXU5bFFPSHVWdER1a1pqbFNNL1Y3dW5YTG5GdHZEeFAiLCJtYWMiOiJhMWNkNTBkYmE2MmMyYmY3NmYyOGQ0YjlmZTVlZjY5YzhhZWFlMDA4YzljMjZlMTc0MDZiYmM1MzkzMzEwNDhiIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6IkhIZ3lWMTRlYklyanZZZVlucUNQcWc9PSIsInZhbHVlIjoiMThuUEVOR2E1THJpV2FVSitHQ1hGWkplVGxPbjdhek9qSGlMeVhzcFZycDI3L21oaFROMllyTzB" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "56bxuk0mCZ0nVKqVOrl8FXU7JX2olV7aEIcokfAX" "uc_cart_id" => "385f979c105eb7f703376339cc2fbec3" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/9751" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 04:57:59GET/chapter/97511121813