f(t)=4t+1 A(x) = (*₁ f(t) dt B(x) = ( ₁² f(t) dt (4) Let C'(x) = 2x² + x. Write C(r) as an integral of f(t) similar to that of A(x) and B(x). (5) Explain, using geometry and area, why if F(t) is any antiderivative of f(t), then the area beneath f(t) on the interval [1, 8] is given by F(8) - F(1).

f(t)=4t+1 A(x) = (*₁ f(t) dt B(x) = ( ₁² f(t) dt (4) Let C'(x) = 2x² + x. Write C(r) as an integral of f(t) similar to that of A(x) and B(x). (5) Explain, using geometry and area, why if F(t) is any antiderivative of f(t), then the area beneath f(t) on the interval [1, 8] is given by F(8) - F(1).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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