MHB Polar coordinates to evaluate double integral

[brunette15]

I am trying to evaluate \int\int xy dxdy over the region R that is defined by r=sin(2theta), from 0<theta<pi/2. I am struggling on where to begin with this. I have tried converting to polar coordinates but am not really getting anywhere. Any guidance would be really appreciated (Crying)

 

[Opalg]

I am trying to evaluate $$\iint xy\, dxdy$$ over the region R that is defined by $$r=\sin(2\theta)$$, from $$0<\theta<\pi/2$$. I am struggling on where to begin with this. I have tried converting to polar coordinates but am not really getting anywhere. Any guidance would be really appreciated (Crying)

Converting to polar coordinates should certainly be the way to go. Can you show what you have done so far, so that we can see why it's "not really getting anywhere"?

The conditions $$r=\sin(2\theta)$$, from $$0<\theta<\pi/2$$, define a closed curve. Presumably the region R is meant to be the region enclosed by this curve. Drawing a rough sketch of R might help you to see what the limits of integration should be, for the polar coordinates.