Answer
(d)
Work Step by Step
Since $x=r\cos \theta $ and $y=r\sin\theta $, where $r: 0\to 1$ and $\theta :0 \to 2\pi$, then $x^2+y^2=r^2\cos^2 \theta+r^2\sin^2 \theta=r^2$. Hence the right integral is $$\int_0^{2\pi}\int_0^1r^3drd\theta.$$ That is, (d) is the right answer.
