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

Homework Help: Trigonometric Substitution Proof

  1. Jul 22, 2008 #1


    User Avatar

    The question is:

    Use [tex]x = \tan \theta , \frac{-\pi}{2} < \theta < \frac{\pi}{2} [/tex] to show that:

    [tex] \int_{0}^{1} \frac{x^3}{\sqrt{x^2+1}} dx =\int_{0}^{\frac{\pi}{4}} \tan^3 \theta \sec \theta d\theta[/tex]

    Using that substitution, I got it down to:

    [tex]\int_{0}^{\frac{\pi}{4}} \frac{\tan^3 \theta}{\sqrt{\tan^2 \theta+1}} = \int_{0}^{\frac{\pi}{4}} \frac{\tan^3 \theta}{\sec \theta}[/tex]

    I have no clue how this is going to get to the answer. Could someone please help? Thanks.
  2. jcsd
  3. Jul 22, 2008 #2


    User Avatar
    Science Advisor
    Gold Member

    What about the dx term?

  4. Jul 22, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    You are forgetting the dx part again. That's why your expression differs from what you are supposed to show. When you get it right, try expressing the integrand in terms of sin and cos.
  5. Jul 23, 2008 #4


    User Avatar

    Ah, NOW I get it. Thanks to everyone for your help!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook