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Integral problem

  1. Jul 20, 2010 #1
    Hello all,

    Can you help me to derive the following integral?

    f(t)=sqrt(r^2-(h*cos(t)-a*sin(t))^2)*(a*cos(t)+h*sin(t))*(h*cos(t)-a*sin(t))

    Integral (f(t),t)?

    Please note that r,h, and a are constant values.

    Any help would be really appreciated.


    Thank you
    Nejla
     
    Last edited: Jul 20, 2010
  2. jcsd
  3. Jul 20, 2010 #2

    mathman

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    Science Advisor
    Gold Member

    The expression looks funny - typos????
     
  4. Jul 21, 2010 #3
    Hopefully this helps. It's the right answer. I checked it in my computer algebra software too.

    integral sqrt(r^2-(h cos(t)-a sin(t))^2) (a cos(t)+h sin(t)) (h cos(t)-a sin(t)) dr =

    1/4 (h cos(t)-a sin(t)) (a cos(t)+h sin(t)) (r sqrt(-2 (a^2+h^2-2 r^2)+2 (a^2-h^2) cos(2 t)+4 a h sin(2 t))-2 (h cos(t)-a sin(t))^2 log(2 sqrt(-2 (a^2+h^2-2 r^2)+2 (a^2-h^2) cos(2 t)+4 a h sin(2 t))+4 r))+constant

    http://www.wolframalpha.com/input/?...))^2)*(a*cos(t)+h*sin(t))*(h*cos(t)-a*sin(t))
     
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