Use FTC II from single-variable calculus to prove the second part of the Fundamental Theorem of Calculus

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Use FTC II from single-variable calculus to prove the second part of the Fundamental Theorem of Calculus for Vector-Valued Functions.

Fundamental Theorem of Calculus for Vector-Valued Functions Part I: If r(t) is continuous on [a, b], and R(1)

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 04, 2024 01:31 PM

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Use FTC II from single-variable calculus to prove the second part of the Fundamental Theorem of Calculus

Question:

Fundamental Theorem of Calculus for Vector-Valued Functions Part I: If r(t) is continuous on [a, b], and R(1) is an antiderivative of r(t), then S." r(t) dt = R(b) - R(a) Part II: Assume that r(t) is continuous on an open interval I and let a be in I. Then d dt r(s) ds = r(t)

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Suppose rt x1 xtxnt Then since differentiation and integration of ...View the full answer

Calculus

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