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AIEEE 2004 Math Solved Paper
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© examsnet.com
Question : 43
Total: 68
The value of
3
∫
−
2
|
1
−
x
2
|
dx
is
1
3
14
3
7
3
28
3
Validate
Solution:
3
∫
−
2
|
1
−
x
2
|
dx
=
3
∫
−
2
|
x
2
−
1
|
dx
Now
|
x
2
−
1
|
=
{
x
2
−
1
if
x
≤
−
1
1
−
x
2
if
−
1
≤
x
≤
1
x
2
−
1
if
x
≥
1
.
∴
Integral is
−
1
∫
−
2
(
x
2
−
1
)
dx
+
1
∫
−
1
(
1
−
x
2
)
dx
+
3
∫
1
(
x
2
−
1
)
dx
[
x
3
3
−
x
]
−
2
−
1
+
[
x
−
x
3
3
]
−
1
1
+
[
x
3
3
−
x
]
1
3
=
(
−
1
3
+
1
)
−
(
−
8
3
+
2
)
+
(
2
−
2
3
)
+
(
27
3
−
3
)
−
(
1
3
−
1
)
=
2
3
+
2
3
+
4
3
+
6
+
2
3
=
28
3
© examsnet.com
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