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This is the integration of pure trigonometric functions. It is based on 3 important rules:
Types of TRIGINT
Type 1 - Straights: These are integrals of simple trigfunctions of the form
or 
or 
.Steps
Example 14
Evaluate
Solution
Example 15
Evaluate
Solution
Type 2 - Prodsums: These are products of trig functions of the form sin mx and cos mx.
Steps
Example 16
Evaluate
Solution
Type 3 - Quotients: These are the integrals of quotients of trig. Functions.
Steps:
Example 17
Evaluate
Solution
Example 18
Evaluate
Solution
Example 19
Evaluate
Solution
Type 4 - Squares: These are products of trig functions of the form
or 
.Steps:
and 
Example 20
Evaluate
Solution
Example 21
Evaluate
Solution
[E] Specials
There are 3 types of integral on the course that require a special substitution:
Type 1 -
This requires the substitution x = a tan u. When this substitution is made the integral turns out to be:
Notes:
To operate these results always make sure that the co-efficient of
is one.Three levels of difficulty exist: Easy (E), Medium (M) and Hard (H).
Example 22 (E)
Evaluate
Solution
Example 23 (M)
Evaluate
Solution
Example 24 (H)
Evaluate
Solution
Type 2 -
This integral requires the special substitution x = a sin u. When the substitution is made the integral turns out to be:
Note: The same notes as for Specials (Type 1) except it can be extended to:
Example 25 (E)
Evaluate
Solution
Example 26 (M)
Evaluate
Solution
Example 27 (H)
Evaluate
Solution
Type 3 -
(The Louser)Unfortunately this integral is not on page 41. You have to make the substitution x = a sin u.
Example 28 (H)
Evaluate
Solution
