Question:medium
$\displaystyle\int_{0}^{\pi/2} \dfrac{\sin^{n}\theta}{\sin^{n}\theta + \cos^{n}\theta}\,d\theta$ is equal to
$\displaystyle\int_{0}^{\pi/2} \dfrac{\sin^{n}\theta}{\sin^{n}\theta + \cos^{n}\theta}\,d\theta$ is equal to
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Standard result: $\displaystyle\int_0^{\pi/2}\frac{\sin^n x}{\sin^n x + \cos^n x}\,dx = \frac{\pi}{4}$ for any $n>0$. This follows from the King's property of definite integrals.
Updated On: Apr 8, 2026
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- $\dfrac{\pi}{2}$
- $\dfrac{\pi}{4}$
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The Correct Option is D
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