Numerical Integration with symbolic integration limits

Hi all,

I am trying to solve the following expression:

exp1=((L+rho)-sqrt(rho^2-(z-(delta+c)/2)^2))^2;

Vg=2*pi*vpaintegral(exp1,z,delta/2,delta+c)

with delta and c being symbolic variables. rho and L depend directly on c.

The problem is that I would like to prescribe a value for Vg and then get a numerical solution for c which is also a part of my integration limits.

Can somebody help me solve this problem? I assume there is a more intelligent way to get a quick solution for this problem.

Thanks!

Answer 1

[Walter Roberson]

You cannot do that. vpaintegral does not support symbolic limits.

You are asking for something like

vpasolve( Vg - 2*pi*vpaintegral(exp1,z,delta/2,delta+c), c)

but you still want delta to be symbolic, so you are looking for c expressed in terms of delta. You cannot get that with numeric techniques. If we had your full formulas then maybe a non-numeric technique could be found.

[Denis Smaitch]

Hi Walter,

thanks for your quick response. Actually, I will be plotting c over delta=a so I could make delta numerical before solving the integral problem. The only sym I am left with during the integration step is c.

syms z delta c a real

theta=deg2rad(30);

alp=acos((a-c)/(a));

rho=(delta+2*a-2*a*cos(alp))/(2*cos(alp+theta));

L=a*sin(alp)-rho*(1-sin(alp+theta));

%% Get volume of gel

exp1=((L+rho)-sqrt(rho^2-(z-(delta+c)/2)^2))^2;

exp2=(z-delta)*(2*a+delta-z);

Vg=vpa(2*pi*vpaintegral(exp1,z,delta/2,delta+c)...

-2*pi*vpaintegral(exp2,z,delta,delta+c),4);

The second part of the integral is easily solvable. The first part is what makes the computation long/imposible.

Thanks for your help!