Mathematics · 2019
JEE Main · 9 January 2019, Shift 1 · Q74
For x^2 ≠ n π+1, n ∈ N (the set of natural numbers), the integral ∫ x √((2 sin (x^2-1)- sin 2(x^2-1))/(2 sin (x^2-1)+ sin 2(x^2-1))) d x is equal to:…
For $\displaystyle x^2 \neq \mathrm{n} \pi+1, \mathrm{n} \in \mathbf{N}$ (the set of natural numbers), the integral
$$\int x \sqrt{\frac{2 \sin \left(x^2-1\right)-\sin 2\left(x^2-1\right)}{2 \sin \left(x^2-1\right)+\sin 2\left(x^2-1\right)}} \mathrm{d} x \text { is }
$$
equal to :
(where c is a constant of integration)
Official answer
(2)
$\displaystyle \log _{\mathrm{e}}\left|\sec \left(\frac{x^2-1}{2}\right)\right|+\mathrm{c}$
(4)
$\displaystyle \frac{1}{2} \log _{\mathrm{e}}\left|\sec ^2\left(\frac{x^2-1}{2}\right)\right|+\mathrm{c}$
NTA’s answer key accepts either.
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JEE Main 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.