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[D] TRIGINT 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 ![]() ![]() ![]() Steps Example 14Evaluate![]() Solution Example 15Evaluate![]() Solution Type 2 - Prodsums: These are products of trig functions of the form sin mx and cos mx. Steps ![]() ![]() ![]() ![]() Example 16Evaluate![]() Solution Type 3 - Quotients: These are the integrals of quotients of trig. Functions. Steps: ![]() Example 17Evaluate![]() Solution Example 18Evaluate![]() Solution Example 19Evaluate![]() Solution Type 4 - Squares: These are products of trig functions of the form ![]() ![]() Steps: ![]() ![]() Example 20Evaluate![]() Solution Example 21Evaluate![]() 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 ![]() 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 - ![]() Unfortunately this integral is not on page 41. You have to make the substitution x = a sin u. Example 28 (H)Evaluate![]() Solution |
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