# Double integral limits after mapping

1. Dec 11, 2012

### nickthegreek

I have the double integral,

∫∫sqrt(x^2+y^2) dxdy, and the area D:((x,y);(x^2+y^2)≤ x)

By completing the squares in D we get that D is a circle with origo at (1/2,0), and radius 1/2. Then I tried changing the variables to x=r cosθ+1/2, y=r sinθ and J(r,θ)=r which leads to a not so nice integrand, and stop.

By changing to polar coordinates directly we get that D transforms into E:((r,θ);r^2≤ r cosθ)) which obv equals r≤cosθ, and the integrand r^3, which is nice. Now to my question. What do I know of "E"? What would it look like? What´s the limits?

Ps. How do I write Latex here?

edit, Ooops, wrong part of the forum? Sry, ill post in the textbook-style problem-part instead...