1. Simpson’s Rule Mini Whiteboards To check your understanding of the video

3. Now work out the values of x 0, x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8.

10. Simpson’s Rule Objectives: To recognise and apply Simpson’s rule to approximate areas bounded by curves.

11. SUMMARY where n is the number of strips and must be even.  The width, h, of each strip is given by  Simpson’s rule for estimating an area is  The accuracy can be improved by increasing n.  a is the left-hand limit of integration and the 1 st value of x.  The number of ordinates ( y -values ) is odd. ( Notice the symmetry in the formula. )

12. Exam Questions

22. Questions about the integral ∫ 0 2 √(1+x 3 )dx. The value of this integral, correct to four decimal places, is 3.2413. Simpson’s rule gives a value of 3.2396 therefore the percentage error is: (a) -0.0525% (b) -0.0524% (c) 0.0524% (d) 0.0525% Integration on GDC

23. Multi guess worksheet You should be ok with questions 1 to 7

24. Exercise D Page 142 Extension: Mixed questions Page 143

25. Simpson’s Rule As before, the area under the curve is divided into a number of strips of equal width. A very good approximation to a definite integral can be found with Simpson’s rule. However, this time, there must be an even number of strips as they are taken in pairs.

26. Simpson’s Rule SUMMARY where n is the number of strips and must be even.  The width, h, of each strip is given by  Simpson’s rule for estimating an area is  The accuracy can be improved by increasing n.  The number of ordinates ( y -values ) is odd. ( Notice the symmetry in the formula. )  a is the left-hand limit of integration and the 1 st value of x.

27. Simpson’s Rule e.g. (a) Use Simpson’s rule with 4 strips to estimate giving your answer to 4 d.p. (b) Use your formula book to help you find the exact value of the integral and hence find an approximation for to 3 s.f. Solution: (a) ( It’s a good idea to write down the formula with the correct number of ordinates. Always one more than the number of strips. )

28. Simpson’s Rule Solution:

29. Simpson’s Rule Solution: (b) The answers to (a) and (b) are approximately equal:

30. Extension 1 2 3

31. 1 2 3