Double integral - me & book ans disagree

**triptyline** · May 27th 2008, 11:30 AM

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 $z=2x+3$ and above the xy-plane and bounded by $y^2=x, x=0, x=2$ .

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

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

Thanks,

triptyline

**galactus** · May 27th 2008, 11:42 AM

Here's the correct set up:

$\int_{0}^{\sqrt{2}}\int_{0}^{y^{2}}(2x+3)dxdy$

**triptyline** · May 27th 2008, 11:50 AM

Yep, your quite right - I've evaluated over the wrong region.

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