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Mathematics
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
\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
\int_{-\sqrt{3}/2}^{\sqrt{3}/2} f(x)\,dx
∫
−
3
/2
3
/2
f
(
x
)
d
x
is : (A)
π
3
−
3
2
\frac{\pi}{3} - \frac{\sqrt{3}}{2}
3
π
−
2
3
(B)
π
3
−
3
4
\frac{\pi}{3} - \frac{\sqrt{3}}{4}
3
π
−
4
3
(C)
π
6
−
3
4
\frac{\pi}{6} - \frac{\sqrt{3}}{4}
6
π
−
4
3
(D)
π
6
−
3
2
\frac{\pi}{6} - \frac{\sqrt{3}}{2}
6
π
−
2
3
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