Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration technique: Multiplication by a form of 1.

  1. Jun 26, 2007 #1
    I would much appriciate if someone could direct me to a webpage that has examples of this. My book, Thomas Calculus, only has one example (elementary) and this is for self study so I don't have lecture notes to go with it. All the questions in it are on trig integrals if that's any help.
  2. jcsd
  3. Jun 26, 2007 #2
    Take the simple case [tex]\int \frac{d\theta}{cos(\theta)}\ [/tex]

    Multiply the integrand by [tex]\frac{cos(\theta)}{cos(\theta)}\ [/tex], which is 1, and you get:

    [tex]\int \frac{cos(\theta)d\theta}{cos^2(\theta)}\ [/tex] = [tex]\int \frac{cos(\theta)d\theta}{1 - sin^2(\theta)}\ [/tex]

    Then, if you put [tex]u = sin(\theta)[/tex], and make all necessary substitutions, the integral becomes:

    [tex]\frac{du}{1 - u^2}\ [/tex]

    Which is trivial to integrate by partial fractions. So hopefully I have shown that multiplication by a form of 1 can be useful in finding integrals that look intimidating such as the integral of sec(x), as above.
    Last edited: Jun 26, 2007
  4. Jun 27, 2007 #3
    Oh I do know it is useful, that's why I want the practice. It's just that I wanted to get more of a feel for how it's done by some examples that are worked through. Worst comes to worst I'll just make some up and back differentiate them and see what happens then.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Integration technique: Multiplication by a form of 1.
  1. Integration Technique (Replies: 12)

  2. Integration Technique (Replies: 2)