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(A) Use Integration by Parts to Prove the Reduction Formula xncosxdx=xnsinxnxn1sinxdx\int x ^ { n } \cos x d x = x ^ { n } \sin x - n \int x ^ { n - 1 } \sin x d x

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(a) Use integration by parts to prove the reduction formula: xncosxdx=xnsinxnxn1sinxdx\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: x4cosxdx\int x ^ { 4 } \cos x d x

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