1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Calc II Integration with trig
  1. Calc II Integral (Replies: 2)

  2. Calc II Integral (Replies: 4)

Loading...