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MHT CET 2017 Math Solved Paper
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© examsnet.com
Question : 9
Total: 50
If
∫
1
√
9
−
16
x
2
dx = α
sin
−
1
(βx) + c, then α +
1
β
=
1
7
12
19
12
9
12
Validate
Solution:
∫
1
√
9
−
16
x
2
d
x
=
∫
1
√
3
2
−
(
4
x
)
2
d
x
=
1
4
∫
1
√
(
3
4
)
2
−
(
x
)
2
d
x
=
1
4
sin
−
1
4
x
3
+
c
[
∵
∫
1
√
a
2
−
x
2
d
x
=
sin
−
1
x
a
+
c
]
As,
∫
1
√
9
−
16
x
2
d
x
=
α
sin
−
1
(
β
x
)
+
c
∴
α
sin
−
1
(
β
x
)
+
c
=
1
4
sin
−
1
(
4
3
x
)
+
c
After comparing on both sides, we get
α
=
1
4
and
β
=
4
3
Hence,
α
+
1
β
=
1
4
+
1
4
3
=
1
4
+
3
4
=
1
© examsnet.com
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