Lesson Plan
Plan: Year 12
Unit: Integration
Lesson: Basic Form of Integration
Estimated time: 40 minutes
Learning objectives
By the end of the sub-unit, students should:
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Understand how integration is the inverse of differentiation
Integrate simple algebraic equations
Evaluate definite integrals
Learning Outcome
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Students will understand how to integrate algebraic equations using rule of basic
integration.
Students will be able to solve integration problems and find the value of 𝑐 in the general
solution of form 𝑓(𝑥) = 𝑎𝑥 𝑛 + 𝑐.
Students will be able to find a solution for definite integrals of simple expressions.
Activity:
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Before beginning this activity, prepare the class by ask the students’ conditions and pray
together
Remind the students about differentiation by giving a differentiation equation (𝑓′(𝑥) =
3𝑥 2 ) and let the students guess the 𝑓(𝑥) form.
Lead the students to create their own definition of integral by doing the activity 1 in the
worksheet.
Explain the form of basic integration by using the differentiation of 𝑓(𝑥) = 𝑥 𝑛 , 𝑓(𝑥) =
1
𝑥 𝑛+1 , and 𝑓(𝑥) = 𝑛+1 𝑥 𝑛+1.
By take a closer look at last equation and explain how reversing it will give them the rule
of integrating𝑥 𝑛 .
Emphasize the rule of basic integrating:
 Add 1 to the power
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 Divide by the new power
 Add a constant
Give some worked examples of integrations (Additional Math book, page 259)
Before continuing to the Definite Integrals, ask the students to do the excercise 15.1 in
page 261, number 3 and disscuss.
Introduce the students about Definite Integral and its two limits, then give a worked
example.
Ask the students to do the excercise 15.2 (page 264) number 1-5 and disscuss the solution
together with the class.
Give a quick review about the integrals as the inverse of differentials, the definition of
indefinite and definite integral.
Before ending the class, remind the students about the assignment that has been given in
the google classroom.
Support:
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Look at the list integrals of standard functions and express the integrands in terms of
these standard functions.
Extend:
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Give challenge to find two different pairs of values of inverse natural logarithms.
Equipment and materials
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Whiteboard, laptop, Geogebra software
Resources
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Cambridge IGCSE and O-Level: Additional Mathematics by Van Hanrahan, Jeanette
Powell, Series editor: Roger Porkess (2018)