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I am required to prove that $\displaystyle \int_0^{2\pi} |x \cos(\theta)+y \sin(\theta)|\, d\theta= 4\sqrt{x^2+y^2}$, $\ x$ and $y$ are real.

I let $\sin\theta = \frac yz$, $\cos\theta=\frac xz$, where $z$ is supposedly complex. Then i managed to show that $x\cos\theta + y\sin\theta = z$, so i am left with integrating $|z|$ (which is the area of a circle?)

I am stuck here since the RHS of what i am supposed to prove, doesn't have pi inside.

Please advise, thanks!!

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    0 = theta! thanks!2012-08-20
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    I edited in Latex and replaced $x$ by $z$ in the denominator of your $\cos\theta$ expression, is this right ? ($x/x$ looked suspicious...)2012-08-20
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    Hi Raymond, yes it is. Thank you so much!2012-08-20
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    you are Welcome !2012-08-20
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    Satisfied with an answer below?2012-09-19

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