[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522912-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522912-en":130},{"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","fundamental-theorem-of-calculus-worksheet-6","Fundamental Theorem of Calculus - Worksheet 6","","This document provides a set of calculus practice problems focused on the application of the Fundamental Theorem of Calculus. It includes eight exercises requiring students to find the derivative F'(x) for various integral-defined functions. Each problem challenges students to utilize the Leibniz integral rule and the chain rule effectively to evaluate functions with variable limits. The worksheet serves as an essential assessment tool for students learning to compute derivatives of functions defined by integrals in advanced mathematics 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is the objective of the problems in this worksheet?","Question",{"text":63,"@type":64},"The primary objective is to find the derivative F'(x) for functions defined by definite integrals.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What mathematical concepts are primarily used to solve these problems?",{"text":68,"@type":64},"Solving these exercises requires the application of the Fundamental Theorem of Calculus and the chain rule for differentiation.",{"name":70,"@type":61,"acceptedAnswer":71},"Does this worksheet provide solutions for the exercises?",{"text":72,"@type":64},"Yes, the document includes the solutions for F'(x) for each of the eight provided integral problems.","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},522912,1791489536,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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\nFundamental Theorem of Calculus Date  Period   \nFor each problem, find F'(x).  \n1) F (x) = x4(t − 1) dt 2) F (x) = x3(t2 + 2t + 3) dt  \n3) F (x) = x12 (−2t + 2) dt 4) F (x) = ∫43x(−t3 + 11t2 − 39t + 44) dt  \n3 2  \n5) F (x) = ∫2x ~~ ~~t13~~ ~~ dt 6) F (x) = ∫xx (−2t − 2) dt  \n7) F (x) = ∫xx2 (t2 − 8t + 11) dt 8) F (x) = ∫x2x2t dt  \nKuta Software-Infinite Calculus  \nFundamental Theorem of Calculus  \nFor each problem, find F'(x).  \n1) F (x) = x4(t − 1) dt  \nF'(x) = x − 1  \nName___________________________________  \nDate________________ Period____  \n2) F (x) = x3(t2 + 2t + 3) dt  \nF'(x) = x 2 + 2x + 3  \n2  \n3) F (x) = x1 (−2t + 2) dt  \nF'(x) = −4x3 + 4x  \n3  \n5) F (x) = ∫2x ~~ ~~t13~~ ~~ dt  \nF'(x) = ~~ ~~3x7~~ ~~  \n2  \n7) F (x) = ∫xx (t2 − 8t + 11) dt  \nF'(x) = 2x5 − 16x3 − x2 + 30x − 11  \n4) F (x) = ∫43x(−t3 + 11t2 − 39t + 44) dt  \nF'(x) = −81x3 + 297x2 − 351x + 132  \n2  \n6) F (x) = ∫xx (−2t − 2) dt  \nF'(x) = −4x3 − 2x + 2  \n8) F (x) = ∫x2x2t dt  \nF'(x) = 0  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiqF6YLtMcEXq","https://ap.wps.com/l/cbCaiqF6YLtMcEXq","pdf",30788,"English","# Calculus Practice Problems\n## Fundamental Theorem of Calculus Exercises","[{\"question\":\"What is the objective of the problems in this worksheet?\",\"answer\":\"The primary objective is to find the derivative F'(x) for functions defined by definite integrals.\"},{\"question\":\"What mathematical concepts are primarily used to solve these problems?\",\"answer\":\"Solving these exercises requires the application of the Fundamental Theorem of Calculus and the chain rule for differentiation.\"},{\"question\":\"Does this worksheet provide solutions for the exercises?\",\"answer\":\"Yes, the document includes the solutions for F'(x) for each of the eight provided integral problems.\"}]","Fundamental Theorem of Calculus - Worksheet 6 | PDF",1791426301]