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Byju's Answer
Standard XII
Mathematics
Integration Using Substitution
∫0ax4 a2-x2 1...
Question
∫
a
0
x
4
(
a
2
−
x
2
)
1
/
2
d
x
equals
A
π
a
5
32
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B
π
a
6
32
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C
π
a
2
32
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D
None of these
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Solution
The correct option is
D
π
a
6
32
I
=
∫
a
0
x
4
√
a
2
−
x
2
d
x
=
∫
a
0
x
5
√
(
a
x
)
2
−
1
d
x
Put
(
a
x
)
2
=
t
⇒
(
−
2
a
2
x
3
)
d
x
=
d
t
I
=
−
∫
1
∞
a
8
t
4
√
t
2
−
1
d
t
=
∫
∞
1
a
8
√
t
2
−
1
√
t
2
d
t
=
a
8
∫
∞
1
√
1
−
1
t
2
d
t
=
π
a
6
32
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3
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-
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is equal to
(a)
2
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(b)
-
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(c)
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(d) none of these