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Indefinite Integrals question

2024 · 29 Jan · Shift 1 · Q43

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JEE Main
Mathematics
Indefinite Integrals
2024 · 29 Jan · Shift 1 · Q43

Indefinite Integrals question

2024 · 29 Jan · Shift 1 · Q43

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

For

x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

, if

y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorname{cosec} x \sec x+\tan x \sin ^2 x} d x

, and

\lim_{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} y(x)=0

then

y\left(\frac{\pi}{4}\right)

is equal to

A
$-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
B
$\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
C
$\frac{1}{2} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
D
$\frac{1}{\sqrt{2}} \tan ^{-1}\left(-\frac{1}{2}\right)$

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