JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

I(m, n)=\int\limits_{0}^1 t^m(1+t)^n d t

then the expression for

I(m, n)

in terms of

I(m+1

n-1

) is

View answer and explanation

Correct option: A

\frac{2^n}{m+1}-\frac{n}{m+1} I(m+1, n-1)

Option A is correct because it is derived using integration by parts, taking

u=(1+t)^n

and

dv=t^m dt

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