# Evaluating an Integral in Polar Coordinates

1. Nov 2, 2013

### PsychonautQQ

1. The problem statement, all variables and given/known data
Evalutate the double integral sin(x^2+y^2)dA between the region 1≥x^2+y^2≥49

3. The attempt at a solution
so r^2 = x^2 + y^2
dA = rdrdθ

so I can turn this into
double integral sin(r^2)rdrdθ
where the inner integral integrated with respect to dr goes from 1 to 7?
and then what are the parameters for integrating with respect to θ? 0 to 2pi?
Does this look correct?

2. Nov 2, 2013

### Sentin3l

To clarify your question: it gives no boundary conditions for your $\theta$ axis, so you are integrating over a disk of radius 7 (starting at 1). So yes your integral seems correct.