Evaluate the double integral
For the function and the region R.
and R is bounded by , , and .

Question

Evaluate the double integral ​  ​
For the function  and the region R.
​  and R is bounded by  ,  ,  and  .
​

Quizplus · Accepted Answer

We can simply evaluate the integral by using polar coordinates. The limits of integration for $r$ will be from $2\cos	heta$ to $2$, and the limits of integration for $	heta$ will be from $0$ to $\pi/2$. Thus, we have:

$$\int_{0}^{\pi/2}\int_{2\cos	heta}^{2}r^2\sin^3\frac{r}{2}\,dr\,d	heta=\frac{64}{15}-\frac{16}{5}\ln 2$$

Therefore, the correct option is B.

Evaluate the Double Integral ​ ​

Evaluate the Double Integral