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Definite integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116210] Definite integral
  • From: carlos at colorado.edu
  • Date: Sat, 5 Feb 2011 05:45:23 -0500 (EST)

Have problems getting Mathematica to compute this
definite integral (length of a parabola, for a graduate homework).
Only completes in reasonable time if theta=0; else freezes.
Any advice? Thanks.

ClearAll[theta,Ls,m,g,=CF=B5,d]; xhat=x/Ls; theta=Pi/6;
H=m*g*Ls^2/(8*d); epsilon=Simplify[m*g*Ls*Sin[theta]/H];
dzhat=xhat*(1-xhat)/2*(1+(epsilon/6)*(1-2*xhat));
zhat=xhat*Tan[theta]+dzhat;
z=zhat*m*g*Sec[theta]*Ls^2/H; z=Simplify[z];
Print["z=",z]; dzdx=Simplify[D[z,x]];
Print["dzdx=",dzdx]; ds=Sqrt[1+dzdx^2];
L=Integrate[ds,{x,0,Ls},Assumptions-
>x>=0&&x<=Ls,Ls>0&&m>0&&g>0&&d>0&&theta>=0];
L=Simplify[L,Ls>0&&L>0]; Print["L=",L//TraditionalForm];


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