Find the volume of the solid whose base is the region between the x-axis and the inverted parabola f(x)=4-x^2 if every vertical cross sections of the solid perpendicular to the y-axis are semicircles.
$\displaystyle V = \int_c^d A(y) \, dy$
$\displaystyle y = 4-x^2$
$\displaystyle x = \sqrt{4-y}$
radius of each semicircular cross section is $\displaystyle x$
$\displaystyle A = \frac{\pi}{2} x^2 = \frac{\pi}{2}(\sqrt{4-y})^2 = $
$\displaystyle V = \frac{\pi}{2}\int_0^4 4-y \, dy$