If , then the value of is equal…

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

If m,n∈Nm,n\in\mathbb{N}, then the value of ∫ab(x−a)m(b−x)n dx\int_a^b(x-a)^m(b-x)^n\,dx is equal to (1) (b−a)m+n m! n!(m+n)!\frac{(b-a)^{m+n}\,m!\,n!}{(m+n)!} (2) (b−a)m+n+1 m! n!(m+n+1)!\frac{(b-a)^{m+n+1}\,m!\,n!}{(m+n+1)!} (3) (b−a)m m!m!\frac{(b-a)^m\,m!}{m!} (4) None of these.

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