[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522918-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522918-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","substitution-for-definite-integrals-calculus-worksheet","Substitution for Definite Integrals - Calculus Worksheet","","This calculus worksheet from Kuta Software focuses on the technique of integration by substitution for definite integrals. It provides a series of practice problems requiring students to express definite integrals in terms of a new variable 'u', as well as problems that require evaluating the integrals after the substitution process. The document serves as an educational resource for students learning advanced calculus, specifically targeting the mastery of u-substitution methods in solving definite integral problems systematically.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/substitution-for-definite-integrals-calculus-worksheet/522918/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/substitution-for-definite-integrals-calculus-worksheet/522918.png","ImageObject",300,407,{"name":42,"@type":43},"นรินทร์","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the primary objective of the exercises in this worksheet?","Question",{"text":63,"@type":64},"The primary objective is to practice expressing definite integrals in terms of the variable 'u' and evaluating those integrals using the substitution method.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Are students required to solve all problems using substitution?",{"text":68,"@type":64},"Yes, the worksheet specifically asks students to use the given substitution (u = ...) to rewrite and evaluate the definite integrals provided.",{"name":70,"@type":61,"acceptedAnswer":71},"Does this worksheet provide solutions for the evaluation problems?",{"text":72,"@type":64},"The document includes partial results for some evaluation problems, such as numerical approximations for the definite integrals.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522918,1791497694,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":96,"preview_page_count":4},2336475104957,"https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787554080175789136","Kuta Software-Infinite Calculus Name___________________________________  \nSubstitution for Definite Integrals Date________________ Period____  \nExpress each definite integral in terms of u, but do not evaluate.  \n1) 01(4x28~~ ~~1)2~~ ~~ dx; u = 4x2 + 1 2) ∫01−12x2 (4x3 − 1) 3 dx; u = 4x3 − 1  \n3) 216x(x2 − 1)2 dx; u = x2 − 1 4) ∫01~~ ~~(4x224)2~~ ~~ dx; u = 4x2 + 4  \nEvaluate each definite integral.  \n5) 03 − ~~ ~~(2x28~~ ~~3)2~~ ~~ dx; u = 2x2 + 3 6) ∫01~~ ~~(4x124)2~~ ~~ dx; u = 4x2 + 4  \n7) 0118x2 (3x3 + 3)2 dx; u = 3x3 + 3 8) ∫01 − ~~ ~~(4x28~~ ~~2)~~ ~~2~~ ~~ dx; u = 4x2 + 2  \nKuta Software-Infinite Calculus Name___________________________________  \nSubstitution for Definite Integrals Date________________ Period____  \nExpress each definite integral in terms of u, but do not evaluate.  \n1) 01(4x28~~ ~~1)2~~ ~~ dx; u = 4x2 + 1 2) ∫01−12x2 (4x3 − 1) 3 dx; u = 4x3 − 1  \n51~~ ~~u12 du 31−u3 du  \n3) x(x2 − 1)2 dx; u = x2 − 1 4) ∫01 (4x224)2  dx; u = 4x2 + 4 033u2 du ∫48~~ ~~3u2 du  \n∫  \nEvaluate each definite integral.  \n5) 03 − ~~ ~~(2x28~~ ~~3)2~~ ~~ dx; u = 2x2 + 3 6) ∫01~~ ~~(4x124)2~~ ~~ dx; u = 4x2 + 4 4 1  \n~~ ~~ ≈ 0.571 ~~ ~~ = 0.25  \n7 4  \n7) 0118x2 (3x3 + 3)2 dx; u = 3x3 + 3 18  \n8) ∫01 − ~~ ~~(4x28~~ ~~2)~~ ~~2~~ ~~ dx; u = 4x2 + 2  \n− ~~ ~~13 ≈ −0.333  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaikJAsQZmGepp","https://ap.wps.com/l/cbCaikJAsQZmGepp","pdf",31311,"English","# Expressing Definite Integrals in Terms of u\n## Evaluating Definite Integrals Using Substitution","[{\"question\":\"What is the primary objective of the exercises in this worksheet?\",\"answer\":\"The primary objective is to practice expressing definite integrals in terms of the variable 'u' and evaluating those integrals using the substitution method.\"},{\"question\":\"Are students required to solve all problems using substitution?\",\"answer\":\"Yes, the worksheet specifically asks students to use the given substitution (u = ...) to rewrite and evaluate the definite integrals provided.\"},{\"question\":\"Does this worksheet provide solutions for the evaluation problems?\",\"answer\":\"The document includes partial results for some evaluation problems, such as numerical approximations for the definite integrals.\"}]","Substitution for Definite Integrals - Calculus Worksheet | PDF",1791426307]