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VITEEE 2018 Solved Paper
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© examsnet.com
Question : 114
Total: 125
The value of
1
∫
−
1
(x - [x]) dx (where [.] denotes greatest integer function) is
0
1
2
None of these
Validate
Solution:
I =
1
∫
−
1
(x - [x]) dx =
1
∫
−
1
xdx -
1
∫
−
1
[x] dx
=
[
x
2
2
]
−
1
1
-
[
0
∫
−
1
[
x
]
d
x
+
1
∫
0
[
x
]
d
x
]
=
1
2
[1 - 1] -
[
0
∫
−
1
[
−
1
]
d
x
+
1
∫
0
[
0
]
d
x
]
[If - ≤ x < 0 , [x] = - 1 ; If 0 ≤ x < 1 , [x] = 0]
= 0 -
[
−
x
]
−
1
0
- 0 = 0 - [ - 0 - ( - 1)] = 1
© examsnet.com
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