Hello, I've been studying double integrals over non-rectangular regions and have been having a bit of trouble but think I've cracked it. However, the book answer and me disagree on the following question; Mathematica agrees with me but I thought maybe I was using the wrong region. The question is:

Find the volume of the solid which is below the plane $\displaystyle z=2x+3$ and above the xy-plane and bounded by $\displaystyle y^2=x, x=0, x=2$.

The region, R, in the xy-plane I'm evaluating over is $\displaystyle R=\{(x,y) | 0 \le y \le x^{1/2}, 0 \le x \le 2\}$ and the final answer I get is $\displaystyle \frac{36}{5} \sqrt{2}$. Whereas the book gets $\displaystyle \frac{14}{5} \sqrt{2}$.

Could somebody verify if I'm using the right region and what the actual answer is?

Thanks,

triptyline