numerical integration n.
Skip this Video
Loading SlideShow in 5 Seconds..
Numerical Integration PowerPoint Presentation
Download Presentation
Numerical Integration

Loading in 2 Seconds...

play fullscreen
1 / 13

Numerical Integration - PowerPoint PPT Presentation

  • Uploaded on

Numerical Integration. Lesson 6.5. News from Space. A new species has been trapped … the rare zoid Math students have long known of efforts of "trapezoid" expeditions Trapezoids were so effective, zoids were thought to be extinct!. a. b. Which dimension is the h?

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

PowerPoint Slideshow about 'Numerical Integration' - theoris

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
news from space
News from Space
  • A new species has been trapped …the rare zoid
  • Math studentshave long known ofefforts of "trapezoid" expeditions
  • Trapezoids were so effective, zoids were thought to be extinct!
trapezoidal rule



  • Which dimension is the h?
  • Which is the b1 and the b2




Trapezoidal Rule
  • Instead of calculatingapproximation rectangleswe will use trapezoids
    • More accuracy
  • Area of a trapezoid

trapezoidal rule1




Trapezoidal Rule
  • Trapezoidal rule approximates the integral
  • Calculator function for f(x)((2*f(a+k*(b-a)/n),k,1,n-1)+f(a)+f(b))*(b-a)/(n*2)trap(a,b,n)
trapezoidal rule2
Trapezoidal Rule
  • Entering the trapezoidal rule into the calculator
  • f(x) must be defined for this to work
trapezoidal rule3
Trapezoidal Rule
  • Try using the trapezoidal rule
  • Check with integration
simpson s rule



Simpson's Rule
  • As before, we dividethe interval into n parts
    • n must be even
  • Instead of straight lines wedraw parabolas through each group of three consecutive points
    • This approximates the original curve for finding definite integral – formula shown below

Snidly Fizbane Simpson

simpson s rule1
Simpson's Rule
  • Our calculator can do this for us also
  • The function is more than a one liner
    • We will use the program editor
    • Choose APPS,7:Program Editor3:New
  • Specify Function,name it simp
simpson s rule2

Local variables discarded when function finishes

Initialize dx

Initialize total with the two end values

Enter commands shown between Func and endFunc

One for loop for the 4* values, one for the 2* values

Return the value

Simpson's Rule
  • Enter the parameters a, b, and n between the parentheses
simpson s rule3
Simpson's Rule
  • Specify a function for f(x)
  • When you call simp(a,b,n),
    • Make sure n is an even number
  • Note the accuracy of the approximation
using data
Using Data
  • Given table of data, use trapezoidal rule to determine area under the curve
    • dx = ?
using data1
Using Data
  • Given table of data, use Simpson's rule to determine area under the curve
  • Lesson 6.5
  • Page 250
  • Exercises 1 – 21 odd