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JEE Main Math Class 12 Integrals Part 3 Questions
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© examsnet.com
Question : 3
Total: 100
If
1
∫
0
1
(
5
+
2
x
−
2
x
2
)
(
1
+
e
(
2
−
4
x
)
)
dx
=
1
α
log
e
(
α
+
1
β
)
,
α
,
β
>
0
, then
α
4
−
β
4
is equal to
[15-Apr-2023 shift 1]
19
-21
21
0
Validate
Solution:
I
=
1
∫
0
d
x
(
5
+
2
x
−
2
x
2
)
(
1
+
e
2
−
4
x
)
.
.
.
(i)
x
→
1
−
x
I
=
1
∫
0
e
2
−
4
x
dx
(
5
+
2
x
−
2
x
2
)
(
1
+
e
2
−
4
x
)
.
.
.
(ii)
Add (i) and (ii)
2
I
1
∫
0
d
x
5
+
2
x
−
2
x
2
=
1
∫
0
d
x
2
(
11
4
−
(
x
−
1
2
)
2
)
I
=
1
√
11
ln
(
√
11
+
1
√
10
)
α
=
√
11
β
=
√
10
α
4
−
β
4
=
121
−
100
=
21
© examsnet.com
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