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Mathematics · 2020
JEE Main · 8 January 2020, Shift 1 · Q60
If ∫ (cos x d x)/(sin^3 x(1+ sin^6 x)^2 / 3)=f(x)(1+ sin^6 x)^1 / λ+c where c is a constant of integration, then λ f((π)/3) is equal to:
If
$$\int \frac{\cos x \mathrm{~d} x}{\sin ^3 x\left(1+\sin ^6 x\right)^{2 / 3}}=f(x)\left(1+\sin ^6 x\right)^{1 / \lambda}+c
$$
where $\displaystyle c$ is a constant of integration, then
$\displaystyle \lambda f\left(\frac{\pi}{3}\right)$ is equal to :
Official answer
(4)
$\displaystyle -2$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.