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Byju's Answer
Standard XII
Mathematics
Higher Order Derivatives
If f : R → ...
Question
If
f
:
R
→
R
,
f
(
x
)
=
x
√
1
+
x
2
&
g
(
x
)
=
(
f
o
f
o
f
o
…
2018
times
(
x
)
)
, find
∫
g
(
x
)
d
x
.
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Solution
f
:
R
→
R
f
(
x
)
=
x
√
1
+
x
2
g
(
x
)
=
f
o
f
o
f
o
.
.
.
.
f
(
x
)
(2018 times)
f
o
f
(
x
)
=
x
√
1
+
x
2
√
1
+
x
2
1
+
x
2
=
x
√
1
+
2
x
2
f
o
f
o
f
(
x
)
=
x
√
1
+
2
x
2
√
1
+
x
2
1
+
2
x
2
=
x
√
1
+
3
x
2
g
(
x
)
=
f
o
f
o
f
o
.
.
.
.
f
(
x
)
=
x
√
1
+
2018
x
2
∫
g
(
x
)
d
x
=
∫
x
d
x
√
1
+
2018
x
2
1
√
2018
∫
x
d
x
√
x
2
+
1
√
2018
=
1
√
2018
√
x
2
+
1
√
2018
=
√
2018
x
2
+
1
2018
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0
Similar questions
Q.
If
f
:
R
+
→
R
+
,
f
(
x
)
=
x
2
+
2
and
g
:
R
+
→
R
+
,
g
(
x
)
=
√
x
+
1
then
(
f
+
g
)
(
x
)
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Q.
If
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)
=
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2
+
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&
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(
x
)
=
m
a
x
{
f
(
t
)
;
0
≤
t
<
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}
, then
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∫
0
g
(
x
)
d
x
=
?
Q.
If
f
:
R
→
R
,
f
(
x
)
=
(
x
+
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2
and
g
:
R
→
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,
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Q.
If f(x) and g(x) are two functions of x, then the integration of product of f(x) and g(x) is: