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Homework Help: Integration HELP!

  1. Nov 21, 2008 #1
    1. Evaluate exactly (in terms of [tex]\pi[/tex]) the definite integral [tex]\int^{\pi/2}_{-\-\pi/2}[/tex] [tex]\frac{dx}{sinx + 2cosx +3}[/tex]

    2. Relevant equations
    How do i do this? Step by step instructions if possible.

    3. The attempt at a solution
    I've tried to manipulate the integral but still don't get anything. I also set the denominator as u. but then i cannot substitute du.

  2. jcsd
  3. Nov 21, 2008 #2
    Substitute trig. objects with parametric formulae:
    sinx=2t/(1+t^2), cosx=(1-t^2)/(1+t^2), dx=2dt/(1+t^2)
    and your trig. integrale becomes the rational integral
    2*Integ[-1,1](1/(t^2+2*t+5)dt = pi/4
  4. Nov 21, 2008 #3


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    That's clever. Took me a moment to figure out why dx= 2dt/(1+t^2).
  5. Nov 21, 2008 #4


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  6. Nov 21, 2008 #5
    awesome... thanks alot guys.

    We didn't spend that much time on that identity so it totally slipped my mind. Thanks for the reminder!
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