1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Integration Problem

  1. Jan 15, 2007 #1
    There's a question here from a past exam paper I don't understand. I have the answer that my lecturer gave but the problem is I just don't really understand it. I'm hoping that another explanation from a different person may help. The question is:


    I'd appreciate any feedback, thanks.
  2. jcsd
  3. Jan 15, 2007 #2


    User Avatar
    Homework Helper

    Let [tex]I_{2n}=\int_{0}^{\frac{\pi}{4}}\tan^{2n}x\, dx[/tex], then

    [tex]I_{2n}=\int_{0}^{\frac{\pi}{4}}\tan^{2n-2}x(\sec^{2}x-1)\, dx=\int_{0}^{\frac{\pi}{4}}\tan^{2n-2}x\sec^{2}x\, dx-\int_{0}^{\frac{\pi}{4}}\tan^{2n-2}x\, dx=\int_{0}^{\frac{\pi}{4}}\tan^{2n-2}x\sec^{2}x\, dx-I_{2n-2}[/tex]​

    now substitute [tex]u=\tan x\Rightarrow du=\sec^{2}x\,dx[/tex] so that [tex]0\leq x\leq \frac{\pi}{4}\Rightarrow 0\leq u\leq 1[/tex] and the integral becomes

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integration Problem
  1. Integration problem (Replies: 3)

  2. Integration problem (Replies: 4)

  3. Integration problems (Replies: 3)

  4. Integral problem (Replies: 3)