Area of fence which base is the path [math]c(t)=(30\cos^3t,30\sin^3t)[/math], with [math]0\leq t\leq \pi[/math], and the height of the fence at [math](x,y)[/math] is the function [math]f(x,y)=1+\frac{y}{3}[/math].

Change the interval where the path is defined.