Answer
$\displaystyle{V=\frac{\pi}{3} }$
Work Step by Step
$\displaystyle{A(x)=\pi(1)^{2}-\pi\left(x^{\frac{1}{4}}\right)^{2}}\\
\displaystyle{A(x)=\pi\left(1-x^{\frac{1}{2}}\right)}$
$\begin{aligned} V &=\int_{0}^{1} A(x) \ d x \\ V &=\int_{0}^{1} \pi\left(1-x^{\frac{1}{2}}\right) \ d x \\ V &=\pi \int_{0}^{1}1-x^{\frac{1}{2}} \ d x \\
V &=\pi\left[x-\frac{2}{3} x^{\frac{3}{2}}\right]_{0}^{1}\\
V &=\pi\left(\left(1-\frac{2}{3}(1)^{\frac{3}{2}} \right)-\left(0 \right)\right) \\ V &=\frac{\pi}{3} \end{aligned}$
