(A) Use Integration by Parts to Prove the Reduction Formula $\int x ^ { n } \cos x d x = x ^ { n } \sin x - n \int x ^ { n - 1 } \sin x d x$

Essay

(a) Use integration by parts to prove the reduction formula: $\int x ^ { n } \cos x d x = x ^ { n } \sin x - n \int x ^ { n - 1 } \sin x d x$ (b) Demonstrate your understanding of this formula by using it to evaluate: $\int x ^ { 4 } \cos x d x$