Estimating the Area Under a Curve Aims: To be able to calculate an estimate for the area under a curve. To decide if this is an over estimate or an under.

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Presentation transcript:

Estimating the Area Under a Curve Aims: 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 a b h

Questions

Estimating What do we mean by estimating? Why might we estimate a value?

Estimating area under curves A B C Below is the graph of y = 10 – x 2 We are interested in finding the area under the curve between x = 0 and x = 3.

y = 10 – x A B 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 C D E F y = 10 – x 2 Area A = Area B = Area C = Total Area = Area D = Area E = Area F =

Slightly Quicker Way el/lib/loadLesson.asp?title=alevel/core2/Integ ration/integration7Trap&taskID= el/lib/loadLesson.asp?title=alevel/core2/Integ ration/integration7Trap&taskID=2060 The explanation on page 2 shows us a slightly quicker way. Example on page 3

Step by Step 1.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 Between x=1 and x=3

Questions Between x=0 and x=3

Questions Between x=-2 and x=2

Questions Between x=1 and x=3

Worksheet questsions