Solving a Complex Integral: Finding the 4

[yoleven]

Homework Statement

$$\int$$$$\int$$_D$$\left|x\right|$$dA
D= X²+y²<=a² where a>0

Homework 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?

 

[zcd]

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

 

[yoleven]

Of course. Thanks.