Calculate volume over area I have a problem with calculating volume of given function over the area.
I enclose an image with my solution, however, I got a bad answer.

According to my book the answer should be pi when I got 2*pi.
Sorry for the quality, I couldn't get better with my phone. Thank you in advance for your help!


There is something wrong in:
$$
\int_0^{2\pi} \int_0^r r(r\cos \phi +1)(r\sin\phi +1) d\phi dr=
\int_0^{2\pi} \int_0^r (r^2\cos \phi +\color{red}r)(r\sin\phi +1) d\phi dr=\\
\int_0^{2\pi} \int_0^r (r^3\sin\phi\cos \phi  +\color{red}r\sin\phi + r^2\cos \phi  +\color{red}r) d\phi dr=\\
\int_0^{2\pi}  \Biggr[ \frac14r^4\sin\phi\cos \phi  +\frac12\color{red}{r^2}\sin\phi + \frac13r^3\cos \phi  +\color{red}{\frac12 r^2}\Biggr]_0^1 d\phi =\\
\int_0^{2\pi}   \frac14\sin\phi\cos \phi  +\frac12\sin\phi + \frac13\cos \phi  +\color{red}{\frac12 } d\phi =
\dots=\pi
$$
