# Homework Help: Double integral polar cordiantes

1. Nov 16, 2012

### christian0710

Hi, I need help with this problem

Evaluate the given integral by changing to polar cordinates

∫∫xydA where D is the disc with centre the origin and radius.

My solution so far.

I believe this would give a circle with radius 3 in xy plane. And then x=r*cos(θ) and y=r*sin(θ)

So ∫(∫((r*cos(θ)*r*sin(θ))*r,r,0,3),θ,0,2∏)

But the result is suppose to be zero.
What am I doing wrong?

2. Nov 16, 2012

### christian0710

Ohh never mind, the result is correct :P
Just me who needs to learn how to use my calculator.

I guess it did not make seance that a circle with radius 3 would give 0 as a result, but perhaps it's because z=x*y --> z=0 <> 0=x*y so x=0/y --> x=0 and y=0/x --y=0
Is that a correct interpretation?

3. Nov 16, 2012

### Staff: Mentor

$$\int_{\theta = 0}^{2\pi}\int_{r=0}^3 rcos(\theta) \cdot rsin(\theta) r~dr~d\theta$$