Let fₙ = ∫₀^(π/2) ( Σ_(k=1)ⁿ sin^(k-1)x) ( Σ_(k=1)ⁿ (2k-1)sin^(k-… | JEE Main 2023 Mathematics PYQ

NVAMediumJEE Main 2023 · 13 April, Shift 2Definite Integrals

Let $f_n = \int_{0}^{\frac{\pi}{2}} \left( \sum_{k=1}^{n} \sin^{k-1}x \right) \left( \sum_{k=1}^{n} (2k-1)\sin^{k-1}x \right) \cos x \, dx$ , $n \in \mathbb{N}$ . Then $f_{21} - f_{20}$ is equal to _____.

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