Integral problem

  • Thread starter nejla
  • Start date
  • #1
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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:

Answers and Replies

  • #2
mathman
Science Advisor
7,970
508
The expression looks funny - typos????
 
  • #3
12
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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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