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Byju's Answer
Standard XII
Mathematics
Property 1
The value of ...
Question
The value of the integral I =
∫
1
0
x
(
1
−
x
)
n
d
x
is
A
1
n
+
1
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B
1
n
+
2
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C
1
n
+
1
−
1
n
+
2
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D
1
n
+
1
+
1
n
+
2
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Solution
The correct option is
C
1
n
+
1
−
1
n
+
2
l
=
∫
1
0
x
(
1
−
x
)
6
n
d
x
l
=
∫
1
0
(
1
−
x
)
x
n
d
x
(
∵
∫
a
0
f
(
x
)
d
x
=
∫
a
0
f
(
a
−
x
)
d
x
)
l
=
(
x
n
+
1
n
+
1
−
x
n
+
2
n
+
2
)
1
0
l
=
1
n
+
1
−
1
n
+
2
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