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Reading Questions: a) According to Part 1 of the Fundamental Theorem of Calculus, which of the following is an antiderivative F for f(x) = x²? (a) √² 2 What is F(2) in the option(s) you picked? 2t dt t² dt (b) [² 2² dt (c) ²². b) You can think of Part 2 of the Fundamental Theorem of Calculus in terms of position s(t) and velocity v(t) = s'(t). Let's assume that v(t) ≥ 0. Explain why [₁ v(t) dt gives the total distance traveled and explain why this equals s(b) – s(a). You may want to look up the Net Change Theorem too.

Reading Questions: a) According to Part 1 of the Fundamental Theorem of Calculus, which of the following is an antiderivative F for f(x) = x²? (a) √² 2 What is F(2) in the option(s) you picked? 2t dt t² dt (b) [² 2² dt (c) ²². b) You can think of Part 2 of the Fundamental Theorem of Calculus in terms of position s(t) and velocity v(t) = s'(t). Let's assume that v(t) ≥ 0. Explain why [₁ v(t) dt gives the total distance traveled and explain why this equals s(b) – s(a). You may want to look up the Net Change Theorem too.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 30E
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Reading Questions: a) According to Part 1 of the Fundamental Theorem of Calculus, which of the following is an antiderivative F for f(x) = x²? (0) [ 20 de (6) fede (o) [in 2t dt b) t² dt t² dt What is F(2) in the option(s) you picked? b) You can think of Part 2 of the Fundamental Theorem of Calculus in terms of position s(t) and velocity v(t) = s'(t). Let's assume that v(t) ≥ 0. Explain why fºu(t). gives the total distance traveled and explain why this equals s(b) – s(a). You may want to look up the Net Change Theorem too.
Transcribed Image Text:Reading Questions: a) According to Part 1 of the Fundamental Theorem of Calculus, which of the following is an antiderivative F for f(x) = x²? (0) [ 20 de (6) fede (o) [in 2t dt b) t² dt t² dt What is F(2) in the option(s) you picked? b) You can think of Part 2 of the Fundamental Theorem of Calculus in terms of position s(t) and velocity v(t) = s'(t). Let's assume that v(t) ≥ 0. Explain why fºu(t). gives the total distance traveled and explain why this equals s(b) – s(a). You may want to look up the Net Change Theorem too.
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