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Byju's Answer
Standard XII
Physics
The Problem of Areas
∫ ex [ 1+sin ...
Question
∫
e
x
[
1
+
sin
x
1
+
cos
x
]
d
x
is equal to
(where
c
is integration constant)
A
e
x
tan
x
2
+
c
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B
e
x
tan
x
2
+
c
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C
e
x
1
+
cos
x
+
c
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D
e
x
[
1
+
sin
(
x
2
)
]
+
c
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Solution
The correct option is
A
e
x
tan
x
2
+
c
I
=
∫
e
x
[
1
+
sin
x
1
+
cos
x
]
d
x
=
∫
e
x
[
1
1
+
cos
x
+
sin
x
1
+
cos
x
]
d
x
We know
1
+
cos
2
x
=
2
cos
2
x
sin
2
x
=
2
sin
x
cos
x
So,
I
=
∫
e
x
[
1
2
sec
2
(
x
2
)
+
tan
(
x
2
)
]
d
x
↓
f
′
(
x
)
↓
f
(
x
)
∴
I
=
e
x
tan
(
x
2
)
+
c
[
∵
∫
e
x
[
f
(
x
)
+
f
′
(
x
)
]
d
x
=
e
x
f
(
x
)
+
c
]
Suggest Corrections
2
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Standard XII Physics
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