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Thread: Hypocycloid Question: why limits go from pi/2 to 0 instead of 0 to pi/2 ?

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    Hypocycloid Question: why limits go from pi/2 to 0 instead of 0 to pi/2 ?

    Can someone please tell me why the lower to upper boundaries go from pi/2 to 0 instead of 0 to pi/2 for the parametric curve. How are the top and bottom integrals equal?
    Last edited by Michael100; 01-03-2018 at 05:01 PM. Reason: Image is kinda hard to see

  2. #2
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    Quote Originally Posted by Michael100 View Post
    Can someone please tell me why the lower to upper boundaries go from pi/2 to 0 instead of 0 to pi/2 for the parametric curve. How are the top and bottom integrals equal?
    The curve is defined by

    x = cos^3(t)
    y = sin^3(t)

    The first integral is the general form for an area. They have replaced y with sin^3(t) and dx with the differential of x = cos^3(t), which is 3cos^2(t)*-sin(t). They therefore had to replace the limits of integration (values of x, namely 0 to 1 to cover the first quadrant) with corresponding values of t: pi/2 at (0,1), and 0 at (1,0).

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