SM025 - 2.2 (Notes Solutions)

2.2 Integration of Trigonometric Functions

Learning Outcomes:

At the end of the lesson, students should be able to

(a) Find the integral of the trigonometric functions

Include:
▪ Constant multiple, sum & differences involving trigonometric
functions , ,

▪ Integration of &

▪ Use of double angle & compound angle formulae

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Basic Trigonometric Integration

Consider

SM025 - 2.2 Page 1

Example 1

Find the following infinite integral:
Solution:

Solution:

Remarks:
Refer to Exercise 2.0 Question 3(a) - (d) for more examples.

SM025 - 2.2 Page 2

Cosine Double Angle Formulae in Integration

Based on
Based on

Example 2

Solutions :

Remarks:
Refer to Exercise 2.0 Question 3(e) - (g) for more examples.

SM025 - 2.2 Page 3

Factor Formulae in Integration

Based on

Based ,

Based on ,

Remarks:

Example 3

Solutions:

Remarks:
Refer to Exercise 2.0 Question 3(h) - (i)
for more examples.

SM025 - 2.2 Page 4

Sine Double Angle Formula in Integration

Based on

Example 4

Solution:

Remarks:
Refer to Exercise 2.0 Question 3(j) for more examples.

SM025 - 2.2 Page 5