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JEE Main Math Class 12 Integrals Part 2 Questions
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© examsnet.com
Question : 11
Total: 100
If
f
:
R
→
R
is given by
f
(
x
)
=
x
+
1
, then the value of
lim
n
→
∞
1
n
[
f
(
0
)
+
f
(
5
n
)
+
f
(
10
n
)
+
.
.
.
.
.
.
.
.
+
f
(
5
(
n
−
1
)
n
)
]
is:
[20 Jul 2021 Shift 2]
3
2
5
2
1
2
7
2
Validate
Solution:
I
=
n
−
1
∑
r
=
0
f
(
5
r
n
)
1
n
I
=
1
∫
0
f
(
5
x
)
d
x
I
=
1
∫
0
(
5
x
+
1
)
d
x
I
=
[
5
x
2
2
+
x
]
0
1
I
=
5
2
+
1
=
7
2
© examsnet.com
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