Course no : EDD 5161E Instructor : Dr. Lee Fong Lok : Mr. Tam Tat Sang Student : Tang Cheuk Hung ( S97094520) Yeung Ka Wai ( S98062090) Group number : 15

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

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

Example : Y = x2

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

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

Y=x2 Y=x2

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

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

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 ]

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

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

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

End of Presentation Thank You!