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Quick question. How do you change the bounds of integration if using sec?

  1. Sep 27, 2012 #1
    And in general, always been bad at it.

    If original bounds are ∫pi/3 to 0 and im changing the bounds because I'm U-substituting.
    My subtitution is u=secx

    so is it when cos = pi/3 and 0 or am I wrong?
    so the new bound would be from pi/2 to pi/3..?
     
  2. jcsd
  3. Sep 27, 2012 #2

    Mentallic

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    the lower bound is [itex]x=\pi/3[/itex] right? And [itex]u=\sec(x)[/itex] so the lower bound after the u-substitution will be [itex]u=\sec(\pi/3)[/itex] and similarly the upper bound will be [itex]u=\sec(0)[/itex]
     
  4. Sep 27, 2012 #3
    just plug in the limits to the substitutition.

    but usually you do not substitute a sec function, usually you would substitute a simpler function.

    gd luck.
     
    Last edited: Sep 27, 2012
  5. Sep 27, 2012 #4
    No the upper bound is pi/3 the lower bound is zero(the number on the bottom of the integral sign is zero). the equation is ∫ dx/ (x^2 times sqrt(4-x^2))
    So you would have to use trig and U substitution( I think)

    with trig sub I got 1/4 ∫csc^2theta

    so you gotta change the bounds. Before you plug anything in.
    u = sec(pi/3) My question was more how do I know what that is. because you can easily find sin, cos with unit circle. but I'm confused how to do it with sec and csc.

    because I have no idea when sec = pi/3 and don't really remember how to figure it out ; /

    because once you change the limits you can just integrate it. which would lead to -1/4 cot

    then you could just plug in those values and find the answer
     
  6. Sep 27, 2012 #5

    Mentallic

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    So with that problem, what did you make your U-sub?

    [tex]\sec(x)=\frac{1}{\cos(x)}[/tex]

    [tex]\csc(x)=\frac{1}{\sin(x)}[/tex]

    [tex]\cot(x)=\frac{1}{\tan(x)}[/tex]

    So then what is [itex]\sec(\pi/3)[/itex] ?

    You're not looking for when "sec" = pi/3, you're looking for sec(pi/3).

    So you were fine with finding specific values of cot(x)?
     
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