The value of k N for which the integral I n =∫₀¹(1-x^(k))ⁿ d x, n N, satisfies 147 I₂₀=148 I₂₁ is

Integral Calculus: JEE Main 2024 Mathematics question

JEE Main 2024 · 8 Apr, Morning shift · Q3484

JEE Main 20248 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

The value of

k \in \mathbb{N}

for which the integral

I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}

, satisfies

147 I_{20}=148 I_{21}

JEE Main 2024 · 8 Apr, Morning shift · Q3484

JEE Main 20248 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

The value of

k \in \mathbb{N}

for which the integral

I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}

, satisfies

147 I_{20}=148 I_{21}