1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Calculus Problem

  1. Jul 17, 2005 #1
    I am having trouble solving this integral:


    I know that x = asin(theta)
    theta = arcsin (x/a)
    d(theta) = 1 / sqrt(4-z^2) dz

    but then I get stuck. Could someone give me a hand?

    ps there should be a number 1 on top of the fraction and the integral has dz after it respectfully. I couldn't get these two in ( It is the first time I used latex) Thanks
  2. jcsd
  3. Jul 17, 2005 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Choose z = asin(theta). With regards to your problem, what should you choose a to be? Differentiate z = asin(theta) to find dz = ?

  4. Jul 18, 2005 #3


    User Avatar
    Science Advisor

    It's the same thing but simpler: let z= 2sin(θ) then dz= 2cos(θ).
    [tex]\frac{1}{(4-z^)^{\frac{3}{2}}}= \frac{1}{8(1- sin^2(\theta))^{\frac{3}{2}}}[/tex][tex]= \frac{1}{8 cos^3(\theta)}[/tex]
    The integral becomes [tex]\frac{1}{8}\integral{\frac{d\theta}{cos^2(\theta)}[/tex].

    The way you were doing it works too, of course.
    Since [tex]d\theta= \frac{dz}{\sqrt{((4-z^2)}}[/tex] and [tex]\frac{1}{(4-z^2)^{\frac{3}{2}}}= \frac{1}{4-z^2}\frac{1}{\sqrt{4-z^2}}[/tex], that gives the same thing.
    Last edited by a moderator: Jul 18, 2005
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook