Notice that the curve given by the parametric equations
x = 81 - t^2
y = t^3 - 25t
is symetric about the x-axis. (If t gives us the point (x,y), then -t will give (x,-y) ).
At which x value is the tangent to this curve horizontal?
The curve makes a loop around the x-axis. What is the total area of this loop?