I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram:(adsbygoogle = window.adsbygoogle || []).push({});

http://www.wolframalpha.com/input/?i=integrate+(r^2(cost^2-sint^2))r+drdt+t=(0)..(pi/2)+r=(1)..(2)+

the integral before I changed it to polar was just ∫_{R}(x^{2}-y^{2})dA where R is the first quadrant region between the circles of radius 1 and 2

mathematically it makes sense that the answer is 0.

but when you draw the picture it is a quarter of a washer in the xy plane. This does not seem like 0 to me. Would someone please explain where my thinking is going wrong?

Thanks

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# Understanding what integrating in polar gives you

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