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NIMCET 2018 Question Paper with solutions
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© examsnet.com
Question : 48
Total: 120
Let f : R → R be defined by f (x) =
{
x
+
2
if
x
<
0
|
x
−
2
|
if
x
≥
0
. Find
3
∫
−
2
f (x) dx
0.5
2.5
4.5
6.5
Validate
Solution:
Given,
f (x) =
{
x
+
2
x
<
0
−
(
x
−
2
)
0
≤
x
<
2
x
−
2
x
>
2
f (x) =
{
x
+
2
x
<
0
2
−
x
0
≤
x
<
2
x
−
2
x
≥
2
∴
0
∫
−
2
f (x) dx +
2
∫
0
f (x) dx +
3
∫
2
f (x) dx
=
0
∫
−
2
(x + 2) dx +
2
∫
0
(2 - x) dx +
3
∫
2
(x - 2) dx
=
[
x
2
2
+
2
x
]
−
2
0
+
[
2
x
−
x
2
2
]
0
3
+
[
x
2
2
−
2
x
]
2
3
=
[
0
−
(
4
2
−
4
)
]
+
[
(
4
−
4
2
)
−
0
]
+
[
(
9
2
−
6
)
−
(
4
2
−
4
)
]
= 2 + 2 -
3
2
+ 2 = 6 -
3
2
=
9
2
= 4.5
© examsnet.com
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