1. Course no : EDD 5161E Instructor : Dr. Lee Fong Lok : Mr. Tam Tat Sang
Student : Tang Cheuk Hung ( S )
Yeung Ka Wai ( S )
Group number : 15

2. Target Audience Subject Topic Form 6 Art & Science students
Average ability
Subject
Mathematics & Statistics
Topic
Trapezoidal Rule

3. We can evaluate by direct integration
But there are many functions like and whose can not be found by direct integration
We use trapezoidal rule to approximate the values of definite integrals

4. Example :
Y = x2

5. Example Con’ t : sum of area of 3 trapeziums 
( by direct integration )

6. Trapezoidal rule with n subintervals
The larger number of subintervals (n) , the better approximation.

7. Y=x2
Y=x2

8. Over estimates / Under estimates
- the approximation > the required area
Y=x2

9. Over estimates / Under estimates
- the approximation < the required area
Y=x 1/2

10. Over estimates / Under estimates
Second Derivative Test
The approximation of the integration is
1. Over estimate on [a , b ] if f “ ( x) > 0 for all x in [a , b ]
2. Under estimate on [a , b ] if f “ ( x) < 0 for all x in [a , b ]

11. Example: The approximation is called Over estimate by Trapezoidal Rule
Y=x2

12. Example:
The approximation is called Under estimate by Trapezoidal Rule
Y=x 1/2

13. Preface to the student I hear …. and I forget I see …. and I remember
I do…. and I understand

14. End of Presentation
Thank You!