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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
The value of ∫0π/2dx(cos⁡x+sin⁡x)4\int\limits_{0}^{\pi / 2} \frac{d x}{(\sqrt{\cos x}+\sqrt{\sin x})^4} is equal to
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Correct option: D
13\frac{1}{3}
Option D (13\frac{1}{3}) is correct because the integral is solved using trigonometric substitution and simplification, resulting in a value of 13\frac{1}{3}.

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