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

Michael100

New member
Joined
Jan 3, 2018
Messages
1
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?
g8lyCfn.jpg
 
Last edited:
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).
 
Top