7 7 approximate integration l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
7.7 Approximate Integration PowerPoint Presentation
Download Presentation
7.7 Approximate Integration

Loading in 2 Seconds...

play fullscreen
1 / 4

7.7 Approximate Integration - PowerPoint PPT Presentation


  • 300 Views
  • Uploaded on

7.7 Approximate Integration. If we wish to evaluate a definite integral involving a function whose antiderivative we cannot find, then we must resort to an approximation technique. We describe three such techniques in this section. Midpoint Rule Trapezoidal Rule Simpson’s Rule. y.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '7.7 Approximate Integration' - libitha


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
7 7 approximate integration
7.7 Approximate Integration

If we wish to evaluate a definite integral involving a function whose antiderivative we cannot find, then we must resort to an approximation technique. We describe three such techniques in this section.

  • Midpoint Rule
  • Trapezoidal Rule
  • Simpson’s Rule
a midpoint rule

y

A. Midpoint Rule

Let f be continuous on [a, b]. The Midpoint Rule for approximating is given by

x

a

b

B. Trapezoidal Rule

y

Let f be continuous on [a, b]. The Trapezoidal Rule for approximating is given by

x

C. Simpson’s Rule (n is even)

y

Let f be continuous on [a, b]. The Simpson’s Rule for approximating is given by

x

example 1
Example 1:

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) the Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)

(a) Trapezoidal Rule

(b) Midpoint Rule

(c) Simpson’s Rule

example 2
Example 2:

The width (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Use Simpson’s Rule to estimate the area of the pool.

6.8

5.6

5.0

7.2

4.8

4.8

6.2

Solutions:

Let x = distance from the left end of the pool

w = w(x) = width at x