Find the area enclosed by the following parametric curves and the x−axis. Find its exact area, no decimals.

Question

{x = 9e^t y= 6t-t^2

Answer 1

a = ∫y dx = ∫ g(t) f'(t) dt
y=0 at t=0,6 so
a = ∫[0,6] (6t-t^2) * 9e^t dt = 14595