1. ## double integral

using polar coordinates evaluate the double integral R=sin(x^2+y^2) dA where R is the region 1 less than or equal to x^2+y^2 less than or equal to 64.

Using polar coordinates evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=144 and x^2-12x+y^2=0.

2. Originally Posted by karnold9
using polar coordinates evaluate the double integral R=sin(x^2+y^2) dA where R is the region 1 less than or equal to x^2+y^2 less than or equal to 64.

Using polar coordinates evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=144 and x^2-12x+y^2=0.
$\iint_D \sin(x^2+y^2)dA=\int_{0}^{8}\int_{0}^{2\pi}r\sin(r ^2)d\theta dr$

Did you draw a graph for the 2nd one. If not it will really help. Here it is.

Note this can be done with out calculus. Good luck.