
Trigonometric Integrals and Substitutions 
This section consists of two parts:
Part I: Trigonometric Integrals. We will distinguish three main cases: Case A: Integrals of type where and are nonnegative integers. METHOD OF INTEGRATION: (i) If is odd, then (ii) If is odd, then (iii) If both and are even, then use the identities or (and) sometimes EXAMPLE 1: Find EXAMPLE 2: Find EXAMPLE 3: Find EXAMPLE 4: Find EXAMPLE 5: Find EXAMPLE 6: Find Case B: Integrals of type where and are nonnegative integers. METHOD OF INTEGRATION: (i) If is odd, then (ii) If is even, then (iii) In other cases the guidelines are not as clearcut. EXAMPLE 7: Find EXAMPLE 8: Find (a) (b) EXAMPLE 9: Find EXAMPLE 10: Find EXAMPLE 11: Find Case C: Integrals of type METHOD OF INTEGRATION: Use the identities EXAMPLE 12: Find Part II: Trigonometric Substitutions. Here we deal with integrals that involve METHOD OF INTEGRATION: (i) If , then (ii) If , then (iii) If , then or EXAMPLE 13: Find EXAMPLE 14: Find EXAMPLE 15: Find EXAMPLE 16: Find EXAMPLE 17: Find EXAMPLE 18: Find EXAMPLE 19: Find EXAMPLE 20: Find Appendix I EXAMPLE 21: Find EXAMPLE 22: Find Appendix II
