Evaluating an Integral in Polar Coordinates

[PsychonautQQ]

Homework Statement

Evalutate the double integral sin(x^2+y^2)dA between the region 1≥x^2+y^2≥49

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?

 

[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.