If $I_n=\int_\limits 0^1 x^n e^{-x} \, d x$ for $n \in N$, then $I_n-n I_{n-1}=$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

I_n=\int\limits_{0}^1 x^n e^{-x} \, d x

for

n \in N

, then

I_n-n I_{n-1}=

View answer and explanation

Correct option: C

-1 / e

Option C (-1 / e) is correct because it is obtained by applying integration by parts to the integral and simplifying the resulting expression.

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