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COMEDK Exam 2022 Solved Paper
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© examsiri.com
Question :
142 of 180
Marks:
+1
,
-0
∫
‌
1
x
√
a
x
−
x
2
‌
dx
is
‌
−
3
a
√
‌
a
−
x
x
+
C
−
‌
2
a
√
‌
x
a
−
x
+
C
‌
−
2
a
√
‌
a
−
x
x
+
C
None of these
Validate
Solution:
Let
I
=
∫
1
x
√
a
x
−
x
2
d
x
Putting
x
=
a
t
⇒
d
x
=
−
a
t
2
d
t
∴
I
=
∫
1
a
t
√
a
.
a
t
−
a
2
t
2
×
−
a
t
2
d
t
=
∫
−
t
t
2
√
a
2
t
−
a
2
t
2
d
t
=
∫
−
1
a
t
√
1
t
=
1
t
2
d
t
=
−
1
a
‌
∫
1
√
t
2
t
−
t
2
t
2
d
t
=
−
1
a
‌
∫
1
√
t
−
1
d
t
=
−
1
a
‌
∫
(
t
−
i
)
−
1
2
d
t
=
−
1
a
(
t
−
1
)
1
2
1
2
+
C
=
−
2
a
(
a
x
−
1
)
1
2
+
C
I
=
−
2
a
√
a
−
x
x
+
C
Option (c) is correct.
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