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Test Index
Indefinite Integrals
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Section:
Mathematics
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© examsnet.com
Question : 60
Total: 83
If ∫
√
1
−
x
2
x
4
dx = A (x)
(
√
1
−
x
2
)
m
+ C , for a suitable chosen integer m and a functionA(x), where C is a constant of integration then
(
A
(
x
)
)
m
equals :
[11 Jan 2019 Shift 1]
-
1
3
x
3
-
1
27
x
9
1
9
x
4
1
27
x
6
Validate
Solution:
∫
|
x
|
√
1
x
2
−
1
x
4
dx ;
Put
1
x
2
- 1 = t ⇒
d
t
d
x
= -
2
x
3
Case 1 : x ≥ 0
-
1
2
‌
∫
√
t
dt ⇒ -
t
3
2
3
+ C
⇒ -
1
2
(
1
x
2
−
1
)
3
2
⇒
(
√
1
−
x
2
)
3
−
3
x
2
+ C
A (x) =
−
1
3
x
2
and m = 3
(
A
(
x
)
)
m
= -
(
1
3
x
3
)
3
= -
−
1
27
x
9
Case-II x ≤ 0
We get
(
√
1
−
x
2
)
3
−
3
x
3
+ C
A (x) =
1
−
3
x
3
, m = 3
(
A
(
m
)
)
m
= -
1
27
x
9
© examsnet.com
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