Page 181 - ADVANCED MATH F.5

Form Five Form Five

Integration

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Introduction

In this chapter, students will learn about the inverse process of
differentiation, integration of functions, and applications of
integration. Guide the students to learn the common methods of
integration: integration by parts, substitution method, inspection
method, and using partial fractions. Also, guide students to
calculate the area under a curve, the area enclosed between two
curves, the area of a sector, the volume of a solid of revolution,
and the length of an arc. The competencies developed have many
real life applications such as determining the total cost and total
revenue of goods produced, finding displacement, velocity and
acceleration of moving bodies, moment of inertia of vehicles,
and the rate of a chemical reaction. It is also used in building
constructions, and in graphical representations where three-
dimensional models are demonstrated in the analysis of spread of
infectious diseases, among many other applications.

Students’ activities
(a) Integrating functions by the substitution method
(b) Integrating functions by parts

(c) Integrating rational functions using partial fractions
(d) Applying integration to determine the area under a curve and
the area enclosed between two curves, volume of a solid of
revolution, and length of an arc

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Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 175