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Homework Help: Calc II Integration with trig

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]\int\frac{dx}{\sqrt{x}\sqrt{1-x}}[/tex]


    2. Relevant equations

    [tex]\int\frac{du}{\sqrt{a^{2}-u^{2}}}= arcsin\frac{u}{a} + C[/tex]

    3. The attempt at a solution

    u[tex]^{2}[/tex]=x

    dx=2u du

    [tex]\int\frac{2u}{u\sqrt{1-u^{2}}}du[/tex]

    2[tex]\int\frac{du}{\sqrt{1-u^{2}}} = 2arcsin\frac{u}{a} + C[/tex]

    =2arcsin([tex]\sqrt{x}[/tex]) + C

    But the book gives the answer to be 2arcsec([tex]\sqrt{x}[/tex]) + C, which I do not understand how they achieved that answer. Any help would be appreciated. Thank you.

    Joe
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 7, 2010 #2
    Well, rest easy.

    I just checked your work and it is definitely [tex]2arcsin(sqrt(x)) + C [/tex]. The answer that was given by the book is an unfortunate typo.

    Also, u = sqrt(x) is another way to use substitution.
     
  4. Sep 8, 2010 #3
    That is good to hear, I felt like I was going crazy. BTW I originally set u=sqrt(x), but when finding du, it was simpler to square both sides. I don't like radicals... Thank you.

    Joe
     
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