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Byju's Answer
Standard XIII
Mathematics
Property 7
The value of ...
Question
The value of
∫
π
/
2
−
π
/
2
cos
x
1
+
e
x
dx
is equal to
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Solution
Let
I
=
∫
π
/
2
−
π
/
2
cos
x
1
+
e
x
dx
Then
,
I
=
∫
π
/
2
0
(
cos
x
1
+
e
x
+
cos
(
−
x
)
1
+
e
−
x
}
dx
(
As
∫
a
−
a
f
(
x
)
dx
=
∫
a
0
(
f
(
x
)
+
f
(
−
x
)
}
dx
]
⇒
I
=
∫
π
/
2
0
(
cos
x
1
+
e
x
+
cos
x
1
+
e
−
x
}
dx
⇒
I
=
∫
π
/
2
0
(
1
1
+
e
x
+
e
x
1
+
e
x
}
cos
x
dx
⇒
I
=
∫
π
/
2
0
(
1
+
e
x
1
+
e
x
}
cos
x
dx
⇒
I
=
∫
π
/
2
0
cos
x
dx
⇒
I
=
(
sin
x
]
π
/
2
0
=
sin
π
2
−
sin
0
=
1
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