Finding unknown limit of integration in MATLAB

Question

I have an equation of the form c = integral of f(t)dt limiting from a constant to a variable (I don't want to show the full equation because it is very long and complex). Is there any way to calculate in MATLAB what the value of that variable is (there are no other variables and the equation is too difficult to solve by hand)?

Answer 1

Assume your limit is from cons to t and g(t) as your function with variable t. Now,

syms t
f(t) = int(g(t),t);

This will give you the indefinite integral. Now f(t) will be

f(t) = f(t)+f(cons);

You have the value of f(t)=c. So just solve the equation

S = solve(f(t)==c,t,'Real',true);

eval(S) will give the answer i think

Answer 2

This is an extremely unclear question - if you do not want to post the full equation, post an example instead

I am assuming this is what you intend: you have an integrand f(x), which you know, and has been integrated to give some constant c which you know, over the limits of x = 0, to x = y, for example, where y may change, and you desire to find y

My advice would be to integrate f(x) manually, fill in the first limit, and subtract that portion from c. Next you could employ some technique such as the Newton-Ralphson method to iteratively search for the root to your equation, which should be in x only

Answer 3

You could use a function handle and the quad function for the integral

myFunc = @(t) exp(t*3); % or whatever
t0 = 0;
t1 = 3;
L = 50;
f = @(b) quad(@(t) myFunc(t,b),t0,t1);
bsolve = fzero(f,2);

Hope it help !