Find the volume of the solid whose base is the region bounded between the curve $y=x^2$ and $x$-axis $[0,2]$ and whose cross-section taken perpendicular to the $x$-axis are squares.
My solution
$$V = \int_0^2\pi f(x)^2\,\mathrm dx = \int_0^2\pi x^4\,\mathrm dx = \frac{32}5\pi$$
But in the book, the answer is $\dfrac{32}5$. Why?