JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

The value of

\int_0^1\left(\prod_{r=1}^n(x+r)\right)\left(\sum\limits_{{k=1}}^n \frac{1}{x+k}\right) d x

equals to

View answer and explanation

Correct option: D

n \cdot n

Option D (

n \cdot n !

) is correct because the integral simplifies to the difference of the product of consecutive integers from 1 to n+1 and 1 to n, which equals

n \cdot n !

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