Question:medium

If $\int_0^{\pi/2}\tan^{14}(x/2)dx = 2\left[\sum_{n=1}^7 f(n) - \frac{\pi}{4}\right]$, then $f(n)=$

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The reduction formula for the definite integral of tangent, $J_m = \int_0^{\pi/4} \tan^m(x) dx$, is $J_m + J_{m-2} = \frac{1}{m-1}$. This is a very useful formula for evaluating integrals of powers of tangent over this specific interval.

Updated On: Mar 30, 2026

$\frac{(-1)^n}{n-1}$
$\frac{(-1)^n}{2n+1}$
$\frac{(-1)^{n+1}}{2n-1}$
$\frac{(-1)^{n+1}}{n+1}$

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The Correct Option is C

Solution and Explanation

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If $\int_0^{\pi/2}\tan^{14}(x/2)dx = 2\left[\sum_{n=1}^7 f(n) - \frac{\pi}{4}\right]$, then $f(n)=$

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The Correct Option is C

Solution and Explanation

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