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More integrating

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data
    A. (1-sin^2x)/(cos^2x) dx
    Upper Limit = pi/4
    Lower Limit = 0

    B. (x-2)/(sqrt x) dx
    Upper Limit = 4
    Lower Limit = 1



    2. Relevant equations



    3. The attempt at a solution
    A. I am having trouble with this one.
    B. (x - 2)/(x^1/2) = (x^1/2 - 2x^-1/2) =
    2/3x^3/2 - 4x^1/2

    I plug in 4 and 1 and I get 2/3
     
  2. jcsd
  3. Nov 24, 2007 #2
    For part a, think about the identity [tex] sin^2x + cos^2x = 1 [/tex]
     
  4. Nov 24, 2007 #3
    Oh I KNEW it!! That was the only thing I could come up with but I wasn't sure if I could do that.

    (1-sin^2x)/(cos^2x) dx

    ummm so I get....

    (cos^2x)/(cos^2x) dx = 1 dx = x??
     
  5. Nov 24, 2007 #4
    That's correct, now just plug in the limits. For part b think about breaking up the one fraction into two fractions, each with the same denominator, then you can use the power rule for integrating.
     
  6. Nov 24, 2007 #5
    A. = pi/4
    B. Do you mean like simplify it? If so then our teacher doesn't want us to simplify at all. If not I don't understand what you mean.
     
  7. Nov 24, 2007 #6
    Ok nevermind, I didn't see that you had already solved it in your first post. It's correct.
     
  8. Nov 24, 2007 #7
    Oh okay...well thank you so much for your help! I have a big test on Monday so I am sure I will be on later but I am too tired right now hehe. Thanks again!
     
  9. Nov 24, 2007 #8
    You're quite welcome, good luck on your test :)
     
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