# Double integral

1. Dec 4, 2009

### yoleven

1. The problem statement, all variables and given/known data
$$\int$$$$\int$$D$$\left|x\right|$$dA
D= X2+y2<=a2 where a>0

2. Relevant equations
$$\int$$$$\stackrel{\Pi/2}{0}$$$$\int$$$$\stackrel{a}{0}$$ r cos $$\Theta$$ r dr d$$\Theta$$

I hope that's clear...

I evaluate this to $$\frac{a^3}{3}$$ sin $$\Theta$$

sin $$\Pi$$/2 = 1

so I get $$\frac{a^3}{3}$$

the book says the answer is 4 $$\frac{a^3}{3}$$

I can't see where the 4 is coming from.

can some one explain this to me?

2. Dec 4, 2009

### zcd

Your domain of [0,pi/2] only includes a quarter of the entire circle.

3. Dec 4, 2009

### yoleven

Of course. Thanks.