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Byju's Answer
Standard XII
Mathematics
Integration of Trigonometric Functions
∫√1+sin x fx ...
Question
If
∫
√
1
+
sin
x
f
(
x
)
d
x
=
2
3
(
1
+
sin
x
)
3
/
2
+
c
,
then
f
(
x
)
equals
A
cos
x
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B
sin
x
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C
tan
x
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D
1
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Solution
The correct option is
A
cos
x
Differentiating both sides, we get
√
1
+
sin
x
f
(
x
)
=
2
3
3
2
(
1
+
sin
x
)
1
/
2
cos
x
⇒
f
(
x
)
=
cos
x
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Similar questions
Q.
∫
√
1
+
sin
x
f
(
x
)
d
x
=
2
3
(
1
+
sin
x
)
3
/
2
+
c
, then
f
(
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)
equals?
Q.
If
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)
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+
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)
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