8. Integration of Trignometric Functions

Calculus 2



Weiqi Zhou

Trignometric Substitutions

Trignometric Substitutions

let ，then ，and

Example

  • compute using trignometric substitutions





  • plug back in

Example

  • compute without using trignometric substitutions





Attention

  • the same anti-derivative may be disguised in different forms

  • the trignometric substitution is a general but not necessarily optimal approach

Exercises

  • compute following indefinite integrals





Summary

  • The substitution formula

  • General strategy