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Question
Mathematics
If [ t ] denotes the greatest integer ≤ t, then the value of (3( e -1)/ e ) ∫ limits12 x2 e[x]+[x3] dx is :
Q. If
[
t
]
denotes the greatest integer
≤
t
, then the value of
e
3
(
e
−
1
)
1
∫
2
x
2
e
[
x
]
+
[
x
3
]
d
x
is :
2413
130
JEE Main
JEE Main 2023
Integrals
Report Error
A
e
8
−
1
0%
B
e
7
−
1
100%
C
e
9
−
e
0%
D
e
8
−
e
0%
Solution:
1
∫
2
x
2
e
[
x
3
]
+
1
d
x
x
3
=
t
3
x
2
d
x
=
d
t
=
3
e
1
∫
8
e
[
t
]
d
t
=
3
e
{
1
∫
2
e
d
t
+
∫
2
3
e
2
d
t
+
……
..
+
7
∫
8
e
7
d
t
}
=
3
e
(
e
+
e
2
+
………
+
e
7
)
=
3
e
2
(
1
+
e
+
………
+
e
6
)
=
3
e
2
(
e
−
1
)
(
e
7
−
1
)
e
3
(
e
−
1
)
1
∫
2
x
2
×
e
[
x
]
+
[
x
3
]
d
x
=
e
3
(
e
−
1
)
×
3
e
2
(
e
−
1
)
(
e
7
−
1
)
=
e
(
e
7
−
1
)
=
e
8
−
e