1. 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.

2. Area of a Trapezium a b h

3. Questions

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

5. Estimating area under curves 10 5 0 1 2 3 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.

6. y = 10 – x 2 10 5 0 1 2 3 A B C Area A = Area B = Area C = Total Area = Will the area calculated be an overestimate or an underestimate?

7. Improving our approximation How can we get a better approximation?

8. 1 2 3 A B C D E F 10 5 0 y = 10 – x 2 Area A = Area B = Area C = Total Area = Area D = Area E = Area F =

9. Slightly Quicker Way http://www.mymaths.co.uk/tasks/library/alev el/lib/loadLesson.asp?title=alevel/core2/Integ ration/integration7Trap&taskID=2060 http://www.mymaths.co.uk/tasks/library/alev 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

10. 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.

11. Questions Between x=0 and x=3 Between x=-2 and x=2 Between x=1 and x=3

12. Questions Between x=0 and x=3

13. Questions Between x=-2 and x=2

14. Questions Between x=1 and x=3

15. Worksheet questsions