Estimating the Area Under a

CurveAims:

To be able to calculate an estimate for the area under a curve.To decide if this is an over estimate or an under estimate.

To consider ways that we can speed up our method.

Area of a Trapezium

hbaA )(2

1

a

b

h

Questions

Estimating• What do we mean by estimating?

• Why might we estimate a value?

Estimating area under curves

10

5

01 2 3

AB

C

Below is the graph of y = 10 – x2

We are interested in finding the area under the curve between

x = 0 and x = 3.

y = 10 – x2

10

5

01 2 3

AB

C

Area A =

Area B =

Area C =

Total Area =

Will the area calculated be an overestimate or an underestimate?

Improving our approximation

How can we get a better approximation?

1 2 3

A B CD

EF

10

5

0

y = 10 – x2Area A =

Area B =

Area C =

Total Area =

Area D =

Area E =

Area F =

Slightly Quicker Way• http://www.mymaths.co.uk/tasks/library/alev

el/lib/loadLesson.asp?title=alevel/core2/Integration/integration7Trap&taskID=2060

• The explanation on page 2 shows us a slightly quicker way.

• Example on page 3

Step by Step1. Sketch the curve with strips drawn on

and x-axis labels.2. Make a table of x and y values.3. Put the y values into the formula:

4. Check your answer is sensible using the calculator.

Questions

Between x=0 and x=3

Between x=-2 and x=2

Betweenx=1 and x=3

Questions

Between x=0 and x=3

Questions

Between x=-2 and x=2

Questions

Betweenx=1 and x=3

Worksheet questsions