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: 8


$$F(x)= \frac{1}{4.4}x^{4.4}-\sqrt{2} x^{\sqrt{2}}+C$$

Work Step by Step

Given $$f(x) = x^{3.4}-2x^{\sqrt{2}-1}$$ Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$ \begin{align*} F(x) &=\frac{x^{4.4}}{4.4}-\frac{2x^{\sqrt{2}}}{\sqrt{2}}+C\\ &= \frac{1}{4.4}x^{4.4}-\sqrt{2} x^{\sqrt{2}}+C \end{align*} To check \begin{align*} F'(x) &=x^{3.4}-2x^{\sqrt{2}-1}\\ &=f(x) \end{align*}
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