Consider the following. [" (a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8. Rg= - 3x) dx (b) Draw a diagram to illustrate the approximation in part (a). (c) Consider the following theorem. If fis integrable on [a, b], then Use this to evaluate the integral. [" f(x) dx = lim x) Ax, where Axb-aand x, -a + 1Ax. DIR 1-1 (d) Interpret the integral part (c) as a difference of areas. O The integral represents the area below the x-axis minus the area above the x-axis. O The integral represents the area above the x-axis minus the area below the x-axis. Illustrate with a diagram. 3 6 5 2 2 2 O
Consider the following. [" (a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8. Rg= - 3x) dx (b) Draw a diagram to illustrate the approximation in part (a). (c) Consider the following theorem. If fis integrable on [a, b], then Use this to evaluate the integral. [" f(x) dx = lim x) Ax, where Axb-aand x, -a + 1Ax. DIR 1-1 (d) Interpret the integral part (c) as a difference of areas. O The integral represents the area below the x-axis minus the area above the x-axis. O The integral represents the area above the x-axis minus the area below the x-axis. Illustrate with a diagram. 3 6 5 2 2 2 O
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Qz7. Please answer this question
![Consider the following.
[²₁x²_
(+²
(a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8.
Rg =
(b) Draw a diagram to illustrate the approximation in part (a).
4
3
2
(c) Consider the following theorem.
- 3x) dx
Use this to evaluate the integral.
4
3
If f is integrable on [a, b], then
2
0-34
1
2
2
for
(d) Interpret the integral in part (c) as a difference of areas.
O The integral represents the area below the x-axis minus the area above the x-axis.
O The integral represents the area above the x-axis minus the area below the x-axis.
Illustrate with a diagram.
y
5
f(x) dx = lim f(x₁) Ax, where Ax =
n→∞2
4
4
i=1
4
3
2
-41
ⒸO-5
b-a and x₁ = a + iAx.
n
2
3
4
2
5
5
X
4
3
7
4
2
2
1
2
O-34
qu
1
3
ⒸO-3¹
3
2
2
13
4
9
2
5
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85bb51a8-92ee-41cc-9a06-62c65f40cedc%2Fbc471f5d-ba07-435d-b3b2-50fadae66be2%2Futxoouc_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following.
[²₁x²_
(+²
(a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8.
Rg =
(b) Draw a diagram to illustrate the approximation in part (a).
4
3
2
(c) Consider the following theorem.
- 3x) dx
Use this to evaluate the integral.
4
3
If f is integrable on [a, b], then
2
0-34
1
2
2
for
(d) Interpret the integral in part (c) as a difference of areas.
O The integral represents the area below the x-axis minus the area above the x-axis.
O The integral represents the area above the x-axis minus the area below the x-axis.
Illustrate with a diagram.
y
5
f(x) dx = lim f(x₁) Ax, where Ax =
n→∞2
4
4
i=1
4
3
2
-41
ⒸO-5
b-a and x₁ = a + iAx.
n
2
3
4
2
5
5
X
4
3
7
4
2
2
1
2
O-34
qu
1
3
ⒸO-3¹
3
2
2
13
4
9
2
5
5
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