Question

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

Answer 1

x=a(t−sint)

y=a(1−cost)
the area, as usual, will be
∫ydx
but notice that
dx / dt=a(1−cost)→dx=a(1−cost)dt

so the integral becomes
∫ydx=∫2π(upper integral limit) 0 (lower integral limit) a^2(1−cost)^2dt