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

question 50

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

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Black Life

Refers to the experiences, culture, and societal contributions of people of African descent.

An American Dilemma

An American Dilemma is a landmark sociological study by Gunnar Myrdal (1944) that addressed the problem of race relations and racial injustice in the United States, highlighting the contradiction between the American ideals of equality and the treatment of African Americans.

Gunnar Myrdal

A Swedish economist and sociologist, known for his influential study on race relations in the United States titled "An American Dilemma" (1944).

Democratic Ideals

Principles that support the belief in equality, freedom, and justice within a societal system where government is carried out by the people, either directly or through elected representatives.