Answer
$\dfrac{9\pi}{280}$
Work Step by Step
We need to integrate the integral as shown below:
$V$=$\int^{n}_{m} A(x) \ dx =\dfrac{\pi}{4}\int^1_0[x-2x^{\frac{5}{2}}+x^4] \ dx \\=\dfrac{\pi}{4}[\dfrac{x^2}{2}-(4/7)x^{\frac{7}{2}}+\dfrac{1}{5} x^5]$
or, $=\dfrac{\pi}{4}(\dfrac{1}{2}-\dfrac{4}{7}+\dfrac{1}{5})$
or, $=\dfrac{9\pi}{280}$
