JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

\alpha \in(0,1)

and

\beta=\log _{e}(1-\alpha)

.
Let

P_{n}(x)=x+\frac{x^{2}}{2}+\frac{x^{3}}{3}+\ldots \frac{x^{n}}{n}, x \in(0,1)

.
Then the integral

\int\limits_{{0}}^{\alpha} \frac{t^{50}}{1-t} d t

is equal to

View answer and explanation

Correct option: A

-\left(\beta+P_{50}(\alpha)\right)

Option A is correct because the integral can be rewritten and evaluated using the given definitions of α, β, and P_n(x).

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