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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
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