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

Simple integral with Trig

  1. Jul 10, 2009 #1


    User Avatar
    Gold Member

    For some reason I cannot see why :

    [tex]\int \sqrt{1+tan^2 \left( \frac{\pi }{4H}} z \right)} dz = \frac{4H}{\pi} sinh^{-1} \left( tan \left[ \frac{\pi z}{4H} \right] \right) [/tex]

    I do not understand so because can't the trig identity [tex] 1+tan^2 \theta = sec^2 \theta [/tex] be used and then the integrand simplifies to:

    [tex] \int sec \left( \frac{\pi z}{4H}} \right) dz [/tex]

    why can't it be done? This leads to a whole different answer obviously...
  2. jcsd
  3. Jul 10, 2009 #2
    No, it doesn't. I just worked out the proof that the result was the same using either method. I encourage you to do the proof yourself, although personally I could not have done it without converting between trigonometric and exponential expressions a few times. If you want I will post the proof.
    Last edited: Jul 10, 2009
  4. Jul 10, 2009 #3


    User Avatar
    Gold Member

    Wait never mind. I now know why when I plugged in the numbers it came out different...calculator was not in radians:rofl::blushing:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Simple integral Trig Date
A Simple integral Jul 4, 2016
Is there a simple integration? Oct 12, 2014
Simple Integration Dec 22, 2013
Simple Integration Orthogonal Sin Nov 21, 2013
Simple? Integration Problem (Trig Sub?) Feb 4, 2008