Question

integrate xydx from x=0 to x=6, given the parametric equations x=6cos z,y=2sin z..z is the angle theta...help plz..

Answer 1

\[\int_0^6xy\;dx=\int_{\cos^{-1}0}^{\cos^{-1}1}(6\cos z)(2\sin z)(-6\sin z\;dz)\]
Assuming 0 ≤ z < π,
\[\int_{\pi/2}^{0}(6\cos z)(2\sin z)(-6\sin z\;dz)\\
72\int_{0}^{\pi/2}\cos z\sin^2 z\;dz\]
Does that help?