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JEE Advanced King's Rule — practice questions

2 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.

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$\displaystyle\int_0^{\pi/2} \dfrac{ in x}{ in x + \cos x}\, dx = ?$$\displaystyle\int_0^\pi \dfrac{x in x}{1 + \cos^2 x}\, dx = ?$