For x (-(π)/2, (π)/2), if y(x)=∫ (cosec x+ sin x)/(cosec x sec x+ tan x sin ² x) d x, and lim x →((π)/2)⁻ y(x)=0 then y((π)/4) is equal to

(A) -1/(√(2)) tan ⁻¹(1/(√(2)))

Integral Calculus: JEE Main 2024 Mathematics question

JEE Main 2024 · 29 Jan, Morning shift · Q4037

JEE Main 202429 Jan, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

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

then

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

is equal to

JEE Main 2024 Integral Calculus Question with Solution (29 Jan Morning shift, Q4037) | JEE Arc