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?
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
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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