Help with Integral Problem: f(t), r, h, a

[nejla]

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

 

[mathman]

The expression looks funny - typos?

 

[rhit2013]

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))