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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
∫
x
(
1
+
x
)
2
d
x
f(x) = \int \frac{\sqrt{x}}{(1+x)^2} dx
f
(
x
)
=
∫
(
1
+
x
)
2
x
d
x
(
x
≥
0
x \ge 0
x
≥
0
). Then
f
(
3
)
−
f
(
1
)
f(3) - f(1)
f
(
3
)
−
f
(
1
)
is equal to (a)
π
12
+
1
2
−
3
4
\frac{\pi}{12} + \frac{1}{2} - \frac{\sqrt{3}}{4}
12
π
+
2
1
−
4
3
(b)
−
π
6
+
1
2
+
3
4
-\frac{\pi}{6} + \frac{1}{2} + \frac{\sqrt{3}}{4}
−
6
π
+
2
1
+
4
3
(c)
−
π
12
+
1
2
+
3
4
-\frac{\pi}{12} + \frac{1}{2} + \frac{\sqrt{3}}{4}
−
12
π
+
2
1
+
4
3
(d)
π
6
+
1
2
−
3
4
\frac{\pi}{6} + \frac{1}{2} - \frac{\sqrt{3}}{4}
6
π
+
2
1
−
4
3
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