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Definite Integration question

2022 · 29 Jul · Shift 1 · Q30

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 29 Jul · Shift 1 · Q30

Definite Integration question

2022 · 29 Jul · Shift 1 · Q30

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The integral

\int\limits_{0}^{\frac{\pi}{2}} \frac{1}{3+2 \sin x+\cos x} \mathrm{~d} x

is equal to :

A
$\tan ^{-1}(2)$
B
$\tan ^{-1}(2)-\frac{\pi}{4}$
C
$\frac{1}{2} \tan ^{-1}(2)-\frac{\pi}{8}$
D
$\frac{1}{2}$

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