Today's calculation of Integral 492
Source: 1978 Aoyama Gakuin University entrance exam
October 7, 2009
calculusintegrationanalytic geometryconicsparabolacalculus computations
Problem Statement
Find the volume formed by the revolution of the region satisfying 0\leq y\leq (x \minus{} p)(q \minus{} x)\ (0 < p < q) in the coordinate plane about the -axis.
You are not allowed to use the formula: V \equal{} \boxed{\int_a^b 2\pi x|f(x)|\ dx\ (a < b)} here.