1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating with radicals

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data
    for the following integrals, am I allowed to break them up like so:

    1. ∫(1)/(sqrt(16-9x²)³) dx

    = ∫(1)/(√16)³ · ∫(1)/(√-9x²)³ dx

    2. ∫(x²)/(sqrt(x²-9)) dx

    = ∫(x²)/(√x²) · ∫(x²)/(√-9) dx

    3. ∫(1)/(x²(sqrt(a²+x²))) dx

    = ∫(1)/(x²) · ∫(1)/(√a²) · ∫(1)/(√x²) dx

    ? ? ?

    2. Relevant equations

    3. The attempt at a solution
    I need to know if I'm allowed to break them up like this before I start attempting a solution
  2. jcsd
  3. Feb 25, 2013 #2


    User Avatar
    Homework Helper

    Is this what you are writing for #1?
    [itex]\int \frac{1}{\left( \sqrt{16-9x^2}\right)^3} dx[/itex]
    [itex]=\int \frac{1}{\left( \sqrt{16}\right)^3} dx \cdot \int \frac{1}{\left( \sqrt{-9x^2}\right)^3} dx[/itex]
    Yikes. No, you cannot do that!

    [itex]\sqrt{a - b} \ne \sqrt{a} \cdot \sqrt{-b}[/itex]
    Better review the properties of radicals.
  4. Feb 25, 2013 #3
    Ok, guess i'll try something else. Thanks
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted