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Standard XII
Mathematics
Integration Using Substitution
Question
Given
∫
2
1
e
x
2
d
x
=
a
,
the value of
∫
e
4
e
√
ln
(
x
)
d
x
is?
e
4
−
e
e
4
−
a
2
e
4
−
a
2
e
4
−
e
−
a
A
e
4
−
e
B
e
4
−
a
C
2
e
4
−
a
D
2
e
4
−
e
−
a
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Solution
Verified by Toppr
Given
∫
2
1
e
x
2
d
x
=
a
,
Let
I
=
∫
e
4
e
√
ln
(
x
)
d
x
Put
ln
(
x
)
=
t
2
⇒
1
x
d
x
=
2
t
d
t
∴
I
=
∫
2
1
e
t
2
.
2
t
2
d
t
=
(
t
e
t
2
)
2
1
−
∫
2
1
e
t
2
d
t
=
2
e
4
−
e
−
a
.
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