Integration of piecewise function with integral

Hi, I have piecewise function J(t,m).

function [j] = functionJ (t,m)

model = @(t) -(0.0008.*m./(-0.01-0.07.*exp(-2.*t))-0.000112.*m.*t.*exp(-2.*t)./(-0.01-0.07.*exp(-2.*t)).^2).*exp(0.0008.*m.*t./(-0.01-0.07.*exp(-2.*t)));

j = (t<20).*((1/20)*integral(model,0,t)) + (t>=20).*((1/20)*integral(model,(t-20),t)); end

Now I need another function R(x,m) to integrate J in respect to t from 0 to x I'm still new with Matlab. Could you please give me hint how to do that?

Answer 1

[Youssef Khmou]

hi, try

 doc quad

 doc trapz

Answer 2

[Andrei Bobrov]

function J = R(f,x,m)
t = x >= 20;
p = zeros(numel(x),1);
p(t) = x(t) - 20;
J = arrayfun(@(x,y)integral(@(t)f(t,m),y,x),x,p);

eg use:

f = @(t,m) -(0.0008.*m./(-0.01-0.07.*exp(-2.*t))-0.000112.*m.*t.*exp(-2.*t)./...
        (-0.01-0.07.*exp(-2.*t)).^2).*exp(0.0008.*m.*t./(-0.01-0.07.*exp(-2.*t)));

m = 1;

x = randi(40,20,1);%eg

out = R(f,x,m)

OR

function J = R(x,m)
t = x >= 20;
p = zeros(numel(x),1);
p(t) = x(t) - 20;
f = @(t,m) -(0.0008.*m./(-0.01-0.07.*exp(-2.*t))-0.000112.*m.*t.*exp(-2.*t)./...
        (-0.01-0.07.*exp(-2.*t)).^2).*exp(0.0008.*m.*t./(-0.01-0.07.*exp(-2.*t)));
J = arrayfun(@(x,y)integral(@(t)f(t,m),y,x),x,p);

ADD

function J = pwint(x,m)
f = @(t,m) -(0.0008.*m./(-0.01-0.07.*exp(-2.*t))-0.000112.*m.*t.*exp(-2.*t)./...
      (-0.01-0.07.*exp(-2.*t)).^2).*exp(0.0008.*m.*t./(-0.01-0.07.*exp(-2.*t)));
t = x >= 20;
p = zeros(numel(x),1);
p(t) = x(t) - 20;
J = arrayfun(@(x,y)integral(@(t)f(t,m),y,x),x,p);

eg use:

R = @(x,m)arrayfun(@(t)integral(@(x)pwint(x,m),0,t,'ArrayValued',true),x);
m = 1;
out = R([30,15],m);

[Lukas]

Thank you for the answer. But this gives me the same result as function J(t,m). I need to integrate J(t,m).

[Andrei Bobrov]

Please, see ADD part in my answer.