CPM Homework Help : CALC Problem 8-7

Evaluate the integral $\int _ { - 1 } ^ { 1 } [ \pi ( - 2 x ^ { 2 } + 2 ) ^ { 2 } - \pi ( - x ^ { 2 } + 1 ) ^ { 2 } ] d x$ .

Hint 1:

Before integrating, factor out the π then expand the integrand.

Hint 2:

Rewrite the expression as follows:
Evaluate.