Answer
$\frac{1}{5}$
Work Step by Step
Since $y = \sqrt[4] x$, then $x = y^4$
We can evaluate the integral to find the area of the region:
$\int_{0}^{1}y^4~dy$
$=\frac{y^5}{5}~\vert_{0}^{1}$
$=(\frac{1^5}{5})-(\frac{0^5}{5})$
$=\frac{1}{5}$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 409: 50
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