For nonzero real numbers r, l and the positive constant number c, consider the curve on the xy plane : y \equal{} \left\{ \begin{array}{ll} x^2 & (0\leq x\leq r) \\
r^2 & (r\leq x\leq l \plus{} r) \\
(x \minus{} l \minus{} 2r)^2 & (l \plus{} r\leq x\leq l \plus{} 2r) \end{array} \right.
Denote V the volume of the solid by revolvering the curve about the x axis. Let r, l vary in such a way that r^2 \plus{} l \equal{} c. Find the values of r, l which gives the maxmimum volume. calculusintegrationcalculus computations