The discussion focuses on evaluating the double integral $$\iint xy\, dxdy$$ over the region defined by the polar equation $$r=\sin(2\theta)$$ for $$0<\theta<\pi/2$$. Participants emphasize the importance of converting Cartesian coordinates to polar coordinates for this evaluation. A suggestion is made to sketch the region R enclosed by the curve to better understand the limits of integration. This approach is crucial for successfully setting up the integral in polar form.
PREREQUISITESStudents and educators in calculus, mathematicians focusing on integral calculus, and anyone looking to deepen their understanding of polar coordinates and double integrals.
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"?brunette15 said: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)