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:
$\int_{0}^{1}y^4~dy$
$=\frac{y^5}{5}~\vert_{0}^{1}$
$=(\frac{1^5}{5})-(\frac{0^5}{5})$
$=\frac{1}{5}$