Consider the following. 2-3x) dx (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). (c) Consider the following theorem. Use this to evaluate the integral. 4 If fis integrable on [a, b], then [" f(x) dx 0-3 lim. Σr(x) x) Ax where Ax-b-a (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. @0-sl 2 dx, = a + Ax. @0-3L 6 @0-14 2 1 2 u u 3 2 2 3 @0-3² 4 @0-3 (
Consider the following. 2-3x) dx (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). (c) Consider the following theorem. Use this to evaluate the integral. 4 If fis integrable on [a, b], then [" f(x) dx 0-3 lim. Σr(x) x) Ax where Ax-b-a (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. @0-sl 2 dx, = a + Ax. @0-3L 6 @0-14 2 1 2 u u 3 2 2 3 @0-3² 4 @0-3 (
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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Qz7. Please answer all the parts to this question
![Consider the following.
(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).
y
5r
4
- 3x) dx
(c) Consider the following theorem.
Use this to evaluate the integral.
4
3
2
If f is integrable on [a, b], then
1
2
2
4
2
5
4
X
(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
•fº"
f(x) dx = lim Σf(x) Ax, where Ax =
n→∞0
i=1
y
5
4
0-3²
4
3
2
O-5
b-a
n
2
2
and x = a + iAx.
3
5₁
4
7
6
5
2
1
1
2
2
2
2
3
3
2
4
4
2
5
4
0-3
2
4
2
U
1
2
3
4
5
X
X
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85bb51a8-92ee-41cc-9a06-62c65f40cedc%2F54202aa0-9781-4c85-8cf7-ca09adea07ed%2F316uneq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following.
(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).
y
5r
4
- 3x) dx
(c) Consider the following theorem.
Use this to evaluate the integral.
4
3
2
If f is integrable on [a, b], then
1
2
2
4
2
5
4
X
(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
•fº"
f(x) dx = lim Σf(x) Ax, where Ax =
n→∞0
i=1
y
5
4
0-3²
4
3
2
O-5
b-a
n
2
2
and x = a + iAx.
3
5₁
4
7
6
5
2
1
1
2
2
2
2
3
3
2
4
4
2
5
4
0-3
2
4
2
U
1
2
3
4
5
X
X
5
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