Numerical Integration with symbolic integration limits

2020 3 23
1 个回答
更新时间：2020 3 23
3 次查看（30 天）

0 个投票

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!

请先登录，再回答此问题。

回答（1 个）

Walter Roberson
Walter Roberson 2020-3-23

0 个投票

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.

1 个评论
显示 -1更早的评论 隐藏 -1更早的评论

Denis Smaitch
Denis Smaitch 2020-3-23
编辑：Denis Smaitch 2020-3-23
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!

请先登录，再进行评论。

类别

在 帮助中心 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by