Calculus 8th Edition

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

Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises - Page 328: 61

Answer

$$29$$

Work Step by Step

Given $$\int_{1}^{4} f^{\prime}(x) d x=17,\ \ \ f(1)= 12$$ By using the Fundamental Theorem of Calculus (2) \begin{aligned} \int_{1}^{4} f^{\prime}(x) d x&=f(4)-f(1)\\ 17&= f(4)-12 \end{aligned} Then \begin{aligned} f(4)&= 17+12\\ &=29 \end{aligned}
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