The object $B\subset\mathbb{R}^3$ is defined by $x^2+y^2\leq1$ and $0\leq z\leq x^2+y^2$. Compute $vol(B)$
My work:
I switched to cylindrical coordinates. so now the equations we get are:
$0\leq r\leq 1\ and\ 0\leq z\leq r^2$
So $vol(B)=\int_0^{2\pi}\int_0^1\int_0^{r^2}rdzdrd\theta=2\pi\int_0^1r^3dr=2\pi/4=\pi/2$. Is this correct or am I missing something here?