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Definite Integration question

2023 · 13 Apr · Shift 2 · Q37

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 13 Apr · Shift 2 · Q37

Definite Integration question

2023 · 13 Apr · Shift 2 · Q37

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f_{n}=\int_{0}^{\frac{\pi}{2}}\left(\sum_{k=1}^{n} \sin ^{k-1} x\right)\left(\sum_{k=1}^{n}(2 k-1) \sin ^{k-1} x\right) \cos x d x, n \in \mathbb{N}

. Then

f_{21}-f_{20}

is equal to

\underline{\hspace{2cm}}

Numerical answer

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