I have to determine the volume generated by rotation around y axis of $y=\sin{(x)}$ for $0\leq x\leq \frac{\pi}{2}$ delimited by the segment on line $y=1$ up to $x=\pi/2$.
The solid that I have to rotate so is
so the formula of rotation of this kind of solid si given by: $$V=\pi\int_{0}^{1}(f(y))^2dy=\pi\int_{0}^{1}\arcsin^2{y}\,\,dy=\frac{1}{4}\pi(\pi^2-8)$$ with x=f(y)
Question: am I right in considering this formula and so the inverse of sine?