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Riemann Sums
Related Topics
Wize University Calculus 2 Textbook > Integration
Riemann Sums
8 Activities
Use the left-endpoint Riemann sum, with
n
=
4
n=4
n
=
4
, to estimate the area under the curve
f
(
x
)
=
e
x
−
x
f\left(x\right)=e^x-x
f
(
x
)
=
e
x
−
x
on the interval
[
1
,
13
]
\left[1,\ 13\right]
[
1
,
13
]
.
3
[
e
+
e
4
+
e
7
+
e
10
]
−
22
3\left[e+e^4+e^7+e^{10}\right]-22
3
[
e
+
e
4
+
e
7
+
e
10
]
−
22
3
[
e
4
+
e
7
+
e
10
+
e
13
]
−
34
3\left[e^4+e^7+e^{10}+e^{13}\right]-34
3
[
e
4
+
e
7
+
e
10
+
e
13
]
−
34
3
[
e
+
e
4
+
e
7
+
e
10
]
−
66
3\left[e+e^4+e^7+e^{10}\right]-66
3
[
e
+
e
4
+
e
7
+
e
10
]
−
66
3
[
e
2
+
e
5
+
e
8
+
e
11
]
−
78
3\left[e^2+e^5+e^8+e^{11}\right]-78
3
[
e
2
+
e
5
+
e
8
+
e
11
]
−
78
3
[
e
4
+
e
7
+
e
10
+
e
13
]
−
102
3\left[e^4+e^7+e^{10}+e^{13}\right]-102
3
[
e
4
+
e
7
+
e
10
+
e
13
]
−
102
I don't know
Check Submission
More Riemann Sums Questions:
Practice: Definite Integral Using Riemann Sums
Evaluate
∫
0
4
(
2
x
2
+
3
)
d
x
\displaystyle \int_{0}^{4}(2x^2 +3)\text{d}x
∫
0
4
(
2
x
2
+
3
)
d
x
using Riemann sums.
Riemann Sums: Approximating Areas
The area bounded by the function
f
(
x
)
f\left(x\right)
f
(
x
)
and the
x
x
x
-axis in the interval
[
a
,
b
]
\left[a,b\right]
[
a
,
b
]
is given by
lim
n
→
∞
∑
i
=
1
n
4
i
n
2
[
e
i
n
]
\displaystyle \lim_{n\to\infty}\sum_{i=1}^n\frac{4i}{n^2}\left[e^{\frac{i}{n}}\right]
n
→
∞
lim
i
=
1
∑
n
n
2
4
i
[
e
n
i
]
.
Determine
f
(
x
)
f(x)
f
(
x
)
,
a
a
a
, and
b
b
b
.
Practice: Definite Integral Using Riemann Sums
Q.
\textbf{Q.}
Q.
Evaluate
∫
0
4
(
2
x
2
+
3
)
d
x
\displaystyle \int_{0}^{4}(2x^2 +3)\text{d}x
∫
0
4
(
2
x
2
+
3
)
d
x
using Riemann sums.