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Math Help - Can someone please explain this integration problem to me?

  1. #1
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    Can someone please explain this integration problem to me?

    I was looking at the proof of the area of a circle in my book and I understood up to the part y = +/- ((r2 - x2)0.5) but then the book said to substitue x with rsin(theta).
    I understood everything that was done after this but what I dont understand is why rsin(theta) was used instead of rcos(theta). If theta is the angle the radius r makes with the x axis in the 1st quadrant, shouldn't x = rcos(theta)? Can someone explain?
    Thanks
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  2. #2
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    Re: Can someone please explain this integration problem to me?

    Actually either \displaystyle \begin{align*} x = r\sin{(\theta)} \end{align*} or \displaystyle \begin{align*} x = r\cos{(\theta)} \end{align*} can be substituted. The whole idea is to make use of the Pythagorean Identity to simplify the integrand to something that can be integrated.
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