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Definite Integration question

2025 · 4 Apr · Shift 1 · Q34

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PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 4 Apr · Shift 1 · Q34

Definite Integration question

2025 · 4 Apr · Shift 1 · Q34

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The value of

\int_{-1}^1 \frac{(1+\sqrt{|x|-x}) e^x+(\sqrt{|x|-x}) e^{-x}}{e^x+e^{-x}} d x

is equal to

A
$1+\frac{2 \sqrt{2}}{3}$
B
$1-\frac{2 \sqrt{2}}{3}$
C
$2+\frac{2 \sqrt{2}}{3}$
D
$3-\frac{2 \sqrt{2}}{3}$

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