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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
If ∫0π/4xsin⁡xcos⁡3x dx=π4+A\int\limits_{0}^{\pi / 4} \frac{x \sin x}{\cos ^3 x} \mathrm{~d} x=\frac{\pi}{4}+A, then AA is equal to
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Correct option: D
−12-\frac{1}{2}
Option D (−12-\frac{1}{2}) is correct because integration by parts and trigonometric identities are used to evaluate the definite integral, resulting in the given value.

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