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Definite Integration question

2023 · 31 Jan · Shift 1 · Q33

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 31 Jan · Shift 1 · Q33

Definite Integration question

2023 · 31 Jan · Shift 1 · Q33

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

\alpha \in (0,1)

and

\beta = {\log _e}(1 - \alpha )

. Let

{P_n}(x) = x + {{{x^2}} \over 2} + {{{x^3}} \over 3}\, + \,...\, + \,{{{x^n}} \over n},x \in (0,1)

. Then the integral

\int\limits_0^\alpha {{{{t^{50}}} \over {1 - t}}dt}

is equal to

A
$- \left( {\beta + {P_{50}}\left( \alpha \right)} \right)$
B
$\beta - {P_{50}}(\alpha )$
C
${P_{50}}(\alpha ) - \beta$
D
$\beta + {P_{50}} - (\alpha )$

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