Re: Definite integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg116213] Re: Definite integral*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Sun, 6 Feb 2011 05:35:05 -0500 (EST)

Carlos, Judging by your equations, you have a cubic curve rather than a parabola. Could this be a mistake? For a cubic curve, you get a fourth order general polynomial under the square root for the computation of the length, so there is no surprise that it is hard to compute. The indefinite integral does actually return an answer, but it is huge and hardly useful for anything. Regards, Leonid On Sat, Feb 5, 2011 at 1:45 PM, <carlos at colorado.edu> wrote: 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]; > >