In this BL session, you will be covering the first few sections of Chapter 6B:
Section 2.1 Definite Integrals
Section 2.2 Area under a Curve as the Limit of a Sum of Areas of Rectangles
Section 2.3 Definite Integral as Area under a Curve
You are to complete the following tasks by Tuesday, 22nd July, 2359 hours.
You will need the Lecture Notes for Chapter 6B Applications of Integration to complete this activity.
For your learning to be effective, please complete the tasks seriously.
LEARNING (30 min )
1. Read your notes, section 2.1. Then watch these videos to fill in your lecture notes Examples 1 - 4 (Pg 2 - 5)
[This section primarily extends from Chapter 6A Integration Techniques, now with upper and lower limits introduced to the integral sign, known as Definite Integrals.
The various standard and special integrals, integrate by substitution and by parts will be revisited here.]
Example 1(i) above
Example 1(ii) (click)
Example 2(i) above
Example 2(ii) (click)
Example 3(i) above
Example 3(ii) (click)
Example 4 (above)
[The key objective is for you to develop the observation how the area under the curve can be approximated by rectangles below and above the actual curve.
Focus on the Left-Hand Sum and Right-Hand sum vis-a-vis the True Area (given by the integral).
You may explore other approximations by various geometrical shapes such as trapezium.
Not to worry about the notations used in the activity. ]
After the above exploration, answer this quiz.
3. Read pages 6 & 7 of your lecture notes (Sections 2.2 and 2.3).
4. Watch the video for Example 5 (Pg 8 - 9).