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\nFundamental Theorem of Calculus Date  Period   \nEvaluate each definite integral.  \n1) 31(−x3 + 3x2 + 1) dx  \n2) 12(x4 + x3 − 4x2 + 6) dx  \n3) ∫13 (2x2 − 12x + 13) dx 4) ∫03 (−x3 + 3x2 − 2) dx  \n5) 01(x5 − 4x3 + 4x + 4) dx 6) 034x13 dx  \n7) −41 − ~~ ~~4x3~~ ~~ dx 8) −314x dx  \n9) ∫ − ~~ ~~π6~~ ~~ 2cos x dx 10) ∫ 22 ~~ ~~x~~ ~~1x~~ ~~2~~ ~~ dx π  \n−  \n4  \n11) −325(2x + 4)~~ ~~13 dx 12) 21(2x~~ ~~~~ ~~4)~~ ~~3~~ ~~ dx  \n13) 11e 2x − 2 dx 14) −42 (−x +  −3x − 9  ) dx  \n15) ∫03 f (x) dx, f (x) = {x2x2 − 16,x + 8, xx  22 16) 15 −  x 2 + 4x  dx  \nKuta Software-Infinite Calculus Name   \nFundamental Theorem of Calculus Date  Period   \nEvaluate each definite integral.  \n1) 31(−x3 + 3x2 + 1) dx  \n12  \n3) ∫13 (2x2 − 12x + 13) dx  \n− ~~ ~~143 ≈ −4.667  \n5) 01(x5 − 4x3 + 4x + 4) dx  \n176 ≈ 2.833  \n2) 12(x4 + x3 − 4x2 + 6) dx  \n17720 = 8.85  \n4) ∫03 (−x3 + 3x2 − 2) dx  \n34 = 0.75  \n6)  \n0  1 3  \n4x dx −3  \n−9 3 3 ≈ −12.98  \n∫  \n7) −41 − ~~ ~~4x3~~ ~~ dx  \n158 = 1.875  \nπ  \n−  \n9) ∫ 6  \n2cos x dx  \nπ  \n−  \n4  \n−1 + 2 ≈ 0.414  \n11) ∫ −25(2x + 4)~~ ~~13 dx −3  \n3  \n− ~~ ~~154~~ ~~2~~ ~~ ≈ −4.725  \n13) ∫ 1 e 2x − 2 dx −1  \ne 4 − 1  \n~~ ~~ ≈ 0.491 2e4  \n15) ∫03 f (x) dx, f (x) ={  \n− ~~ ~~53 ≈ −1.667  \n8) −314x dx  \n−4 ln 3 ≈ −4.394  \n10) ∫ 22 ~~ ~~x~~ ~~1x~~ ~~2~~ ~~ dx  \nπ12 ≈ 0.262  \n12) 21(2x~~ ~~~~ ~~4)~~ ~~3~~ ~~ dx  \n11528 ≈ 0.117  \n14) −42 (−x +  −3x − 9  ) dx 9  \nx2 − 1, x2 − 6x + 8,  \nx ≤ 2  \nx > 2  \n16) 15 −  x 2 + 4x  dx  \n− ~~ ~~463 ≈ −15.333  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaigeKAKvgti71","https://ap.wps.com/l/cbCaigeKAKvgti71","pdf",58274,"English","# Calculus Problems\n## Definite Integral Worksheet\n## Detailed Solutions and Results","[{\"question\":\"What is the primary focus of this worksheet?\",\"answer\":\"The worksheet focuses on practicing the evaluation of definite integrals using the First Fundamental Theorem of Calculus.\"},{\"question\":\"What types of functions are included in the problem set?\",\"answer\":\"The problems cover a variety of mathematical functions, including polynomials, trigonometric functions (such as cosine), exponential functions, and piecewise-defined functions.\"},{\"question\":\"Are there solutions provided for the practice problems?\",\"answer\":\"Yes, the document includes a comprehensive answer key that provides both exact and decimal approximations for all 16 integration problems.\"}]","Fundamental Theorem of Calculus - Worksheet and Solutions | PDF",1791426296]