MCQMediumJEE Main 2023 · 31 January, Shift 1Indefinite Integrals

Mathematics Question from JEE Main 2023 · 31 January, Shift 1

Let α∈(0,1)\alpha \in (0, 1) and β=log⁡(1−α)\beta = \log(1 - \alpha). Let

Pn(x)=x+x22+x33+⋯+xnn,x∈(0,1).P_n(x) = x + \frac{x^2}{2} + \frac{x^3}{3} + \cdots + \frac{x^n}{n}, \quad x \in (0, 1).

Then the integral

∫0αt501−t dt\int_0^\alpha \frac{t^{50}}{1 - t} \, dt

is equal to:

  • A

    β−P50(α)\beta - P_{50}(\alpha)

  • B

    −(β+P50(α))-(\beta + P_{50}(\alpha))

  • C

    P50(α)−βP_{50}(\alpha) - \beta

  • D

    P50(α)P_{50}(\alpha)

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