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

1. ## 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?

2. Originally Posted by Michael100
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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