Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.9 Antiderivatives - 3.9 Exercises - Page 282: 16


$$F(t) = 3\sin t+4\cos t+C $$

Work Step by Step

Given $$f(t) = 3\cos t-4\sin t$$ Then by using table 2 if $f(x)=\sin x\ \to\ \ F(x) =-\cos +C$ and if $f(x)=\cos x\ \to\ \ F(x) =\sin x +C$ Hence \begin{align*} F(t) &= 3\sin t+4\cos t+C \end{align*} To check \begin{align*} F'(t) &= 3\cos t-4\sin t\\ &=f(t) \end{align*}
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