In this question, you will estimate the value of the integral c9 [²² using three different approximations. xe-5 da dx a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following Ax = 2 ao 3 a₁ = 5 a2 7 f(ao): = 3e f(a₁) = f(a₂) a3 = 9 f(a3) X1 = 4 f(x₁) = X2 = 6 f(x₂)= X3 = 8 f(x3) b. Calculate the approximate value of the integral using the trapezoidal rule. Area 4.7981 c. Calculate the approximate value of the integral using the midpoint rule. Area 4.8438 d Calculate the approximato value of the integral using Simpson's rule II = = = X
In this question, you will estimate the value of the integral c9 [²² using three different approximations. xe-5 da dx a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following Ax = 2 ao 3 a₁ = 5 a2 7 f(ao): = 3e f(a₁) = f(a₂) a3 = 9 f(a3) X1 = 4 f(x₁) = X2 = 6 f(x₂)= X3 = 8 f(x3) b. Calculate the approximate value of the integral using the trapezoidal rule. Area 4.7981 c. Calculate the approximate value of the integral using the midpoint rule. Area 4.8438 d Calculate the approximato value of the integral using Simpson's rule II = = = X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Help would be much apprecited! Thank you.
![In this question, you will estimate the value of the integral
c9
[²²
using three different approximations.
xe-* da
a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following
Ax = 2
ao
3
a₁ = 5
a2
7
f(ao): = 3e
f(a₁) =
f(a₂)
a3
= 9
f(a3)
X1 = 4
f(x₁) =
X2 = 6
f(x₂)=
X3 = 8
f(x3)
b. Calculate the approximate value of the integral using the trapezoidal rule.
Area
4.7981
c. Calculate the approximate value of the integral using the midpoint rule.
Area
4.8438
d. Calculate the approximate value of the integral using Simpson's rule.
Area 4.457
II
=
=
=
e. It is possible to show that an antiderivative of x e**/3 is
−3 (x+3) e-
333
X
Using this antiderivative, calculate the exact value of the integral.
Integral = 4.8297](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d7e592c-743b-41ca-8c45-a73d8bec675b%2F4d06e85d-6d4b-4561-80af-9ba1bec7d1dc%2Fdiahc8_processed.png&w=3840&q=75)
Transcribed Image Text:In this question, you will estimate the value of the integral
c9
[²²
using three different approximations.
xe-* da
a. Subdivide the interval [3,9] into three sub-intervals of equal width and complete the following
Ax = 2
ao
3
a₁ = 5
a2
7
f(ao): = 3e
f(a₁) =
f(a₂)
a3
= 9
f(a3)
X1 = 4
f(x₁) =
X2 = 6
f(x₂)=
X3 = 8
f(x3)
b. Calculate the approximate value of the integral using the trapezoidal rule.
Area
4.7981
c. Calculate the approximate value of the integral using the midpoint rule.
Area
4.8438
d. Calculate the approximate value of the integral using Simpson's rule.
Area 4.457
II
=
=
=
e. It is possible to show that an antiderivative of x e**/3 is
−3 (x+3) e-
333
X
Using this antiderivative, calculate the exact value of the integral.
Integral = 4.8297
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)