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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
x
2
+
2
x
g(x)=x^{2}+2x
g
(
x
)
=
x
2
+
2
x
. Using
N
N
N
equal subintervals on
[
0
,
2
]
[0,2]
[
0
,
2
]
and right endpoints, express
∫
0
2
g
(
x
)
d
x
\displaystyle \int_{0}^{2} g(x)\,dx
∫
0
2
g
(
x
)
d
x
as
lim
N
→
∞
∑
i
=
1
N
(
⋅
)
\displaystyle \lim_{N\to\infty}\sum_{i=1}^{N}(\,\cdot\,)
N
→
∞
lim
i
=
1
∑
N
(
⋅
)
, and simplify the summand completely so that it contains only
i
i
i
and
N
N
N
(no
x
x
x
).
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