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: 18


$$G(v) =5v+3\tan v+C $$

Work Step by Step

Given $$g(v) = 5+ 3\sec^2v$$ Then by using table 2 if $f(x)= x^n\ \to\ \ F(x) = \frac{x^{n+1}}{n+1} +C$ and if $f(x)=\sec^2x\ \to\ \ F(x) =\tan x +C$ Hence \begin{align*} G(v)&=5v+3\tan v+C \end{align*} To check \begin{align*} G'(v) &= 5+ 3\sec^2v\\ &=g(v) \end{align*}
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