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Definite Integration question

2021 · 20 Jul · Shift 2 · Q35

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PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 20 Jul · Shift 2 · Q35

Definite Integration question

2021 · 20 Jul · Shift 2 · Q35

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

g(t) = \int_{ - \pi /2}^{\pi /2} {\cos \left( {{\pi \over 4}t + f(x)} \right)} dx

, where

f(x) = {\log _e}\left( {x + \sqrt {{x^2} + 1} } \right),x \in R

. Then which one of the following is correct?

A
g(1) = g(0)
B
$\sqrt 2 g(1) = g(0)$
C
$g(1) = \sqrt 2 g(0)$
D
g(1) + g(0) = 0

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