Question

find the area between the cycloid : x=a(t-sint), y=a(1-cost) [0 14 years ago

Answer 1

\[x=a(t-\sin t)\]\[y=a(1-\cos t)\]the area, as usual, will be\[\int ydx\]but notice that\[\frac{dx}{dt}=a(1-\cos t)\to dx=a(1-\cos t)dt\]so the integral becomes\[\int ydx=\int_{0}^{2\pi}a^2(1-\cos t)^2dt\]

Answer 2

Saved me again .. i wonder why i didn't get there myself .. you make it look so simple ! =]