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WBJEE 2015 Math Solved Paper
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© examsnet.com
Question : 54
Total: 80
Let f(x) denote the fractional part of a real number x. Then the value of
√
3
∫
0
f(
x
2
) dx
2
√
3
-
√
2
- 1
0
√
2
-
√
3
+ 1
√
3
-
√
2
+ 1
Validate
Solution:
√
3
∫
0
f(
x
2
) dx =
√
3
∫
0
{
x
2
} dx
=
√
3
∫
0
(
x
2
- [
x
2
]) dx
=
√
3
∫
0
x
2
dx -
(
1
∫
0
[
x
2
]
dx
+
√
2
∫
1
[
x
2
]
dx
+
√
3
∫
√
2
[
x
2
]
dx
)
=
√
3
- (
1
∫
0
0.dx+
√
2
∫
1
1.dx+
√
3
∫
√
2
2.dx)
=
√
3
- (
√
2
- 1 + 2
√
3
- 2
√
2
) =
√
2
-
√
3
+ 1
© examsnet.com
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