1. The mid-ordinate rule Aims:
To be able to estimate the area under curves using the mid-ordinate rule.
To know when the solution gives an underestimate or an overestimate.
To know how to make your approximation more accurate.

2. The mid ordinate rule
Calculates an approximation for the area under a curve by splitting it up into rectangles.
Which one will give the best estimate?

3. The mid ordinate rule
Uses the midpoint as the height of the rectangle.
This gives a part that is an underestimate and a part that is an overestimate.
Add up the area of all the rectangles to get an approximation.
Width
Sum of mid-ordinates

4. Example
Use the mid-ordinate rule with 6 strips to calculate an approximation to Give your answer to 3 s.f.
1) Sketch
2) Table
3) Sub in values

5. To the worksheet….

6. How can we improve accuracy?
Review so far….
How can we improve accuracy?
More Strips!!

7. Underestimate or overestimate?
Even though part of this cancels down not all does as the underestimated part is not the same size as the overestimated part.
Overestimate
Underestimate

8. Some questions to set up yourselves…
2. Use the mid-ordinate rule

9. Question 1 Solution

10. Question 2 Solution

11. Plenary
Are the following hypotheses true:
In cases where the trapezium rule gives an underestimate, the mid-ordinate rule gives an overestimate, and vice versa.
In any given case, the magnitude of the error using the mid-ordinate rule is less than that using the trapezium rule.