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JEE Advanced 2014 Paper 2 Mathematics Q1
Mathematics
Problem
The function
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
is the solution of the differential equation
d
y
d
x
+
x
y
x
2
−
1
=
x
4
+
2
x
1
−
x
2
\displaystyle \frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}
d
x
d
y
+
x
2
−
1
x
y
=
1
−
x
2
x
4
+
2
x
in
(
−
1
,
1
)
(-1,1)
(
−
1
,
1
)
satisfying
f
(
0
)
=
0
f(0)=0
f
(
0
)
=
0
. Then
∫
−
3
/
2
3
/
2
f
(
x
)
d
x
\displaystyle \int_{-\sqrt3/2}^{\sqrt3/2} f(x)\,dx
∫
−
3
/2
3
/2
f
(
x
)
d
x
is
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