How to combine functions?

Hi! I am working on a code where I have 3 functions that overtake from each other at t=0 to 5, 5 to 15.4 and 15.4 to 25.

later I am trying to integrate them using the trapezoidal rule, but before I tried to combine 3 functions with poly2sum function. But my integral appears as x10^24 which is definitely not correct. Does anyone know how can I use trapezoidal rule to intregrate these 3 functions when t= as described above or how to combine them into 1 function?

Please need help

clc,clear,close all
f=[];
for t=1:25
    if t<5
        f(t)=0.1553567*(t.^6) - 2.0416*(t.^5) + 9.1837*(t.^4) - 14.829*(t.^3) - 1.3703*(t.^2) + 32.821*(t) - 1.3155;
    elseif (t>=5)&&(t<15.4)
        f(t)=0.003980879*(t.^5) - 0.2247*(t.^4) + 4.8682*(t.^3) - 50.442*(t.^2) + 254.67*(t) - 430.66;
    elseif t>=15.4
        f(t)=-0.073*(t.^2) + 6.1802*(t) + 40.423;
    end
end
syms t
plot(f)
xlabel('Time(s)')
ylabel('Speed(mph)')
grid on
title('Speed(mph) vs Time(s)')
f1=f;
c=poly2sym(f,t); 
f=@(t) (3181181871604081*t.^24)/140737488355328 + (2235201853553569*t.^23)/70368744177664 + (799700918963229*t.^22)/17592186044416 + (3923588293415859*t.^21)/70368744177664 + (1093666568987161*t.^20)/17592186044416 + (1279362089076253*t.^19)/17592186044416 + (1364564885566369*t.^18)/17592186044416 + (1425048751384133*t.^17)/17592186044416 + (1500543524306005*t.^16)/17592186044416 + (1603138970636933*t.^15)/17592186044416 + (1725688668888861*t.^14)/17592186044416 + (1850213893459389*t.^13)/17592186044416 + (1956307498310429*t.^12)/17592186044416 + (2029537800646613*t.^11)/17592186044416 + (2069852464594085*t.^10)/17592186044416 + (1060968907371289*t.^9)/8796093022208 + (8753125867013119*t.^8)/70368744177664 + (4504113319202993*t.^7)/35184372088832 + (2313263393287229*t.^6)/17592186044416 + (592975416952619*t.^5)/4398046511104 + (2427971483171239*t.^4)/17592186044416 + (2481472839369517*t.^3)/17592186044416 + (1266202868202655*t.^2)/8796093022208 + (5161540348557237.*t)/35184372088832 + 1313283076494721/8796093022208;
a = 1; 
b = 9;
d_exact = integral(f,a,b); % exact distance
%% TRAPEZOIDAL RULE
Fa = f(a); 
Fb = f(b);              % first and last elements
err = Inf;              % intitial absolute error
n = 1;                  % number of sections
i = 1; % iteration
while err >= 0.00002
    h = (b-a)/n; 
    t = a;
    sigma = 0;
    for k = 1:n-1 
        t = t+h;
        sigma = sigma + f(t); 
    end
    d_approx = (h/2)*(Fa+ 2*sigma + Fb); 
    err = abs(d_exact-d_approx)/d_exact; 
    no_sec(i) = n; 
    distance(i) = d_approx; 
    Err_pert(i) = err*100; 
    i = i + 1;
    n = 2*n; 
end

fprintf('\nn(sections)\t\tD(m)\tRelative Error(%%)')
for i=1:numel(no_sec)
    fprintf('\n\t%d\t\t\t%0.e\t\t%0.3f',no_sec(i),distance(i),Err_pert(i))
end
fprintf('\n\n')

%% b)
t = linspace(a,b,25);
v = f1;
dist = v.*t;
figure;
subplot(2,1,1)
plot(v)
title('Speed vs Time')
xlabel('t(s)')
ylabel('Speed(m/s)')
grid on
subplot(2,1,2)
plot(dist)
title('Distance vs Time')
xlabel('T(s)')
ylabel('Distance(m)')
grid on

%% c)
figure;
semilogx(no_sec,distance)
xlabel('Sections [n]')
ylabel('Distance (m)')
grid on

Answer 1

[Michael Gareis]

Try defining your equation with piecewise(). https://www.mathworks.com/help/symbolic/piecewise.html