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Definite Integration question

2021 · 27 Aug · Shift 2 · Q34

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PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 27 Aug · Shift 2 · Q34

Definite Integration question

2021 · 27 Aug · Shift 2 · Q34

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The value of the integral

\int\limits_0^1 {{{\sqrt x dx} \over {(1 + x)(1 + 3x)(3 + x)}}}

is :

A
${\pi \over 8}\left( {1 - {{\sqrt 3 } \over 2}} \right)$
B
${\pi \over 4}\left( {1 - {{\sqrt 3 } \over 6}} \right)$
C
${\pi \over 8}\left( {1 - {{\sqrt 3 } \over 6}} \right)$
D
${\pi \over 4}\left( {1 - {{\sqrt 3 } \over 2}} \right)$

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