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Differential Equations question

2014 · Shift 2 · Q33

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JEE Advanced
Mathematics
Differential Equations
2014 · Shift 2 · Q33

Differential Equations question

2014 · Shift 2 · Q33

JEE AdvancedMathematicsDifferential EquationsMCQ+3 / −1

The function

y=f(x)

is the solution of the differential equation

{{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{{x^4} + 2x} \over {\sqrt {1 - {x^2}} }}\,

in

(-1,1)

satisfying

f(0)=0

. Then

\int\limits_{ - {{\sqrt 3 } \over 2}}^{{{\sqrt 3 } \over 2}} {f\left( x \right)} \,d\left( x \right)

is

A
${\pi \over 3} - {{\sqrt 3 } \over 2}$
B
${\pi \over 3} - {{\sqrt 3 } \over 4}$
C
${\pi \over 6} - {{\sqrt 3 } \over 4}$
D
${\pi \over 6} - {{\sqrt 3 } \over 2}$

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