simpson’s rule mini whiteboards to check your understanding of the video

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

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Simpson’s Rule

Mini Whiteboards

To check your understanding of

the video

Now work out the values of x0, x1, x2, x3, x4, x5, x6, x7, x8.

Simpson’s Rule

Objectives:To recognise and apply Simpson’s

rule to approximate areas bounded by

curves.

SUMMARY

where n is the number of strips and must be even.

n

abh

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 1st value of x.

nnn

b

a

yyyyyyyyh

ydx 1243210 42...24243

The number of ordinates ( y-values ) is odd.

( Notice the symmetry in the formula. )

Exam Questions

Questions about the integral ∫02 √(1+x3)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

Multi guess worksheet

You should be ok with questions 1 to 7

Exercise DPage 142

Extension:Mixed questions

Page 143

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.

Simpson’s RuleSUMMARY

where n is the number of strips and must be even.

n

abh

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.

nnn

b

a

yyyyyyyyh

ydx 1243210 42...24243

The number of ordinates ( y-values ) is odd.

( Notice the symmetry in the formula. )

a is the left-hand limit of integration and the 1st value of x.

Simpson’s Rule

1

021

1dx

x

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) 43210 424

3yyyyy

hA

( It’s a good idea to write down the formula with the correct number of ordinates. Always one more than the number of strips. )

Simpson’s Rule

1750502500 x

Solution:

2504

01,4

hn

1

021

1dx

x 43210 4243

yyyyyh

50640809411801 y

) d.p. ( 478540

1

021

1dx

x 43210 424

3

250yyyyy

Simpson’s RuleSolutio

n:(b)

1

021

1dx

x 101tan x

0tan1tan 11

4

The answers to (a) and (b) are approximately equal:

785404

So,

) s.f. 3( 143

Extension1

2

3

Extension1

2

3