Mathematics · 2022
JEE Main · 26 July 2022, Shift 2 · Q19
The integral ∫ ((1-1/(√ 3))( cos x- sin x))/((1+2/(√ 3) sin 2 x)) d x is equal to
The integral $\displaystyle \int \frac{\left(1-\dfrac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\dfrac{2}{\sqrt{3}} \sin 2 x\right)} d x$ is equal to
Official answer
(1)
$\displaystyle \frac{1}{2} \log _e\left|\frac{\tan \left(\dfrac{x}{2}+\dfrac{\pi}{12}\right)}{\tan \left(\dfrac{x}{2}+\dfrac{\pi}{6}\right)}\right|+C$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.