(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: $\int x ^ { 4 } \cos x d x$

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The Answer of (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: $\int x ^ { 4 } \cos x d x$

(A) Use Integration by Parts to Prove the Reduction Formula ∫xncos⁡xdx=xnsin⁡x−n∫xn−1sin⁡xdx\int x ^ { n } \cos x d x = x ^ { n } \sin x - n \int x ^ { n - 1 } \sin x d x∫xncosxdx=xnsinx−n∫xn−1sinxdx

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