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MHTCET 2016 Math Solved Paper
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© examsnet.com
Question : 27
Total: 50
If
∫
f
(
x
)
log
(
sin
x
)
d
x
=
log
[
log
sin
x
]
+
c
,
then
f
(
x
)
is equal to
cot x
tan x
sec x
cosec x
Validate
Solution:
(a)
∫
f
(
x
)
log
(
sin
x
)
d
x
=
log
[
log
sin
x
]
+
c
After differentiating on both sides, we get
f
(
x
)
log
(
sin
x
)
=
1
log
sin
x
d
d
x
(
log
sin
x
)
+
0
⇒
f
(
x
)
log
(
sin
x
)
=
1
log
sin
x
×
1
sin
x
×
cos
x
⇒
f
(
x
)
=
cot
x
© examsnet.com
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