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Byju's Answer
Standard XII
Mathematics
Definite Integral as Limit of Sum
lim r =1 n n ...
Question
l
i
m
n
→
∞
∑
n
r
=
1
n
n
2
+
r
2
x
2
,
x
>
0
is equal to :
A
t
a
n
−
1
x
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B
x
t
a
n
−
1
x
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C
t
a
n
−
1
x
x
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D
t
a
n
−
1
x
x
2
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Solution
The correct option is
C
t
a
n
−
1
x
x
l
i
m
n
→
∞
∑
n
r
=
1
n
n
2
+
r
2
x
2
=
l
i
m
n
→
∞
∑
n
r
=
1
1
n
(
1
+
(
r
n
)
2
x
2
)
=
∫
1
0
d
t
1
+
t
2
x
2
=
1
x
2
∫
1
0
d
t
(
1
x
)
2
+
t
2
=
1
x
2
.
1
1
/
x
[
t
a
n
−
1
(
1
1
/
x
)
]
1
0
=
1
x
t
a
n
−
1
x
=
t
a
n
−
1
x
x
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0
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