Recent content by 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

Thank you all. I eventually solved my problem. Whenever I get the chance, I will write down its answers here.Nejla

Hi again, I tried it for a special case where plane1 is x=0 and I got the right answer. But for the general case where plane1 is ax+by+cz+d=0, I cannot calculate the integrals. For the general case I have: x1=- d/a - (b*y)/a - (c*z)/a x2=(r^2 - x^2 - y^2)^(1/2) y1=-(a*(a^2*r^2 - a^2*z^2 +...

Dear all, I do really need your help. I'd like to find the volume contained between a sphere (x^2+y^2+z^2=r^2) , plane1 (ax+by+cz+d=0), and plane2 (z-h=0). Would you please check what I've done till now? From the sphere and plane1 equations I got: x1=sqrt*(r^2-y^2-z^2) x2=d/a-(b/a)y-(c/a)z...

Dear Eynstone, Thank you sooooo much. You are generous. No DOUBT. I asked this question because I wanted to solve another problem and now it seems that it is more complicated than what I was expecting. May I ask you about that question? How can I find the volume of the intersection of two...

Dear all, How can I derive the volume of a spherical cap by integration and using the Cartesian coordinate system. The sphere is located at the (0,0,0) coordinates and its radius is set to r. The height of the cap is also set to (r-h). I googled a lot but I couldn't find it. I would...