Section Summary: 8.3

1. Definitions

   None.

2. Theorems

   None.

3. Properties/Tricks/Hints/Etc.

   Remember your trig identities!

   

   Note that you have to pay attention to the interval on which you make the substitution.

4. Summary

   Trig substitution is defined as a method of ``inverse substitution'': rather than replace some complex function of the dummy variable with a new variable u, e.g.

   

   we replace the dummy variable of integration x by some complex function of u! Hence, we might try

   

   and hope that things turn out nicer.

   In particular, this section demonstrates that root functions can sometimes be eliminated using this technique.