Integration
     TRIGONOMETRICIDENTITIES
            Graham S McDonald
             and Silvia C Dalla
        Aself-contained Tutorial Module for practising
        integration of expressions involving products of
        trigonometric functions such as sinnxsinmx
  ●Table of contents
  ●Begin Tutorial
   c
  
2004 g.s.mcdonald@salford.ac.uk
           Table of contents
   1. Theory
   2. Exercises
   3. Answers
   4. Standard integrals
   5. Tips
    Full worked solutions
     Section 1: Theory                                                    3
     1. Theory
     Integrals of the form      Z
                                  sinnxsinmx,
     and similar ones with products like sinnxcosmx and cosnxcosmx,
     can be solved by making use of the following trigonometric identities:
                sinAsinB = −1[cos(A+B)−cos(A−B)]
                                   2
               sinAcosB = 1[sin(A+B)+sin(A−B)]
                                 2
               cosAcosB = 1[cos(A+B)+cos(A−B)]
                                 2
     Using these identities, such products are expressed as a sum of
     trigonometric functions
     This sum is generally more straightforward to integrate
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   Section 2: Exercises                  4
   2. Exercises
   Click on EXERCISE links for full worked solutions (9 exercises in
   total).
   Perform the following integrations:
   Exercise 1.
   Z cos3xcos2xdx
   Exercise 2.
   Z sin5xcos3xdx
   Exercise 3.
   Z sin6xsin4xdx
      ●Theory●Standard integrals ● Answers ● Tips
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