Oh yeah I really live this.
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I imagine you were just so exited to say that you love this that you accidentally wound up saying something much more profound
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Polar coordinates were the bane of my existence. :D So glad as a computer engineer vs electrical engineer I never have to do them again. How the heck does the 0 to 2 pi integration just = 2 pi?
And how do you integrate around a circle if the function doesn't exist for y < 0? 
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The function does exist for y<0 :D And the reason it’s just 2π is because the integrand only depends on r, not φ
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I'm so mad that I don't get this!! Wish I'd had help with math when I was young.
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I too was no good at math in high school.. never too late!
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I never tried this trick with non-infinite limits of integration, does it work?
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Not for this integral, no.
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And this is why most humans hate higher mathematics!
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Oh nooo! :(
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