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Byju's Answer
Standard XII
Mathematics
Definition of Limit
∫a + cb + c f...
Question
∫
b
+
c
a
+
c
f
(
x
)
d
x
is equal to
A
∫
b
a
f
(
x
−
c
)
d
x
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B
∫
b
a
f
(
x
+
c
)
d
x
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C
∫
b
a
f
(
x
)
d
x
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D
∫
b
+
x
a
+
x
f
(
x
)
d
x
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Solution
The correct option is
B
∫
b
a
f
(
x
+
c
)
d
x
Since by putting
x
=
t
+
c
,
we get
When
x
=
a
+
c
⟹
t
=
a
and when
x
=
b
+
c
⟹
t
=
b
So,
I
=
∫
b
a
f
(
c
+
t
)
d
t
Putting
t
=
x
, we get:
=
∫
b
a
f
(
x
+
c
)
d
x
.
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