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AIEEE 2003 Math Solved Paper
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© examsnet.com
Question : 37
Total: 66
The value of the integral
I
=
1
∫
0
x
(
1
−
x
)
n
dx
is
1
n
+
1
+
1
n
+
2
1
n
+
1
1
n
+
2
1
n
+
1
−
1
n
+
2
Validate
Solution:
I
=
1
∫
0
x
(
1
−
x
)
n
dx
=
1
∫
0
(
1
−
x
)
(
1
−
1
+
x
)
n
dx
=
1
∫
0
(
1
−
x
)
x
n
dx
=
[
x
n
+
1
n
+
1
−
x
n
+
2
n
+
2
]
0
1
=
1
n
+
1
−
1
n
+
2
© examsnet.com
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