Integration and Evaluation of Simple Algebraic Functions – SS3 Mathematics Lesson Note (Second Term)

Integration is the inverse operation of differentiation, also called anti-differentiation. To integrate a power, add one (1) to the power and divide by the new power, using the general integral formula. This works in the same way that multiplication and division, or raising to a power and extracting roots, undo each other.

Behavioural objectives

By the end of the lesson, students should be able to:

1. Define integration.
2. Distinguish between integration and differentiation.
3. Apply the integration formula.

Instructional resources

Chart showing rules of integration.

Lesson procedure

Step 1: Identification of prior ideas

Mode: Individual

Teacher’s activities: The teacher asks the students to carry out the following operations:

1. 5 + 3 = ?
2. 5 + 2 = ?
3. 2232 = ?
4. 6422 = ?

Step 2: What is integration?

Mode: Whole class

Teacher’s activities: The teacher explains to the students that integration can simply be defined as adding one (1) to the power and dividing by the new power, using the formula below, where it is a constant.

Multiplication and division are inverse operations, and so are raising to a power and extracting roots. In the same way, we develop the inverse operation of differentiation, called anti-differentiation (integration), using indices.

Step 3: Application

Mode: Whole class

Teacher’s activities: The teacher asks the students to solve the following on the board.

Integrate

Student activities: The students integrate the function.

Evaluation

Mode: Whole class

The teacher evaluates the lesson with the following questions:

1. Define integration.
2. State the general integral formula.
3. Explain how integration is related to differentiation.

Assignment

1. Write down the general integral formula.
2. In your own words, state the rule for integrating a power.

Reference

• New general mathematics for SS3
• New concept mathematics for SS3