Download presentation
Presentation is loading. Please wait.
1
4.6 Numerical Integration Trapezoid and Simpson’s Rules
2
Trapezoidal Rule To estimate the definite integral, we will divide the Interval into “n” trapezoids.
4
The Trapezoidal Rule Let f be a continuous function on [a,b]. Then the Trapezoidal Rule for estimating the definite integral is given by
![The Trapezoidal Rule Let f be a continuous function on [a,b].](http://images.slideplayer.com/22/6419604/slides/slide_4.jpg "Then the Trapezoidal Rule for estimating the definite integral is given by.")
6
Use the Trapezoid Rule to approximate the definite integral for the given “n”.
7
Use the Trapezoid Rule to approximate the definite integral. Compare results when n=3 and n=6
8
Simpsons Rule (with an even “n”) Let f be a continuous function on [a,b]. Simpson’s Rule for estimating the definite integral is given by
![Simpsons Rule (with an even n ) Let f be a continuous function on [a,b].](http://images.slideplayer.com/22/6419604/slides/slide_8.jpg "Simpson’s Rule for estimating the definite integral is given by.")
9
Use Simpsons Rule to approximate
10
HOMEWORK Pg 314: 2-14even, 19
Similar presentations
![1 Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's Rules using the regular partition P of the interval [0,2] into 6 subintervals. (b) Find.](/19/5867193/big_thumb.jpg "1 Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's Rules using the regular partition P of the interval [0,2] into 6 subintervals. (b) Find.>")
