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.