function main
clear all %OK in main function

afun = inline('exp(t)./(t.^3+1)','t');
tstep = .1; %time increment
tmax = 10; %max time value to consider

%method 1 - trapz
tic;
t = 0:tstep:tmax;
a = afun(t); %compute a for all values of t
v0 = -2; %initial velocity
n=1;
v = v0; %current velocity at t(n)

while (v<10 & n<length(t))
  n = n + 1;
  v = v0 + trapz(t(1:n),a(1:n));
end
printans(v,t(n),'trapz');

%method 2 - cumtrapz and find
tic;
vv = v0 + cumtrapz(t,a);
ii = find(vv>10);
if (length(ii)>0)
    n = ii(1);
else
    n = length(t);
end
printans(vv(n),t(n),'cumtrapz');


%method 3 - quad8
tic;
tt = 0;
v = v0;
while (v<10 & tt<tmax)
  tt = tt + tstep;
  v = v0 + quad8(afun,0,tt);
end

printans(v,tt,'quad8');

return


function printans(v,t,meth)
fprintf('\n-------\n');
fprintf('Method: %s\n',meth);
fprintf('Compute time: %.2f\n',toc);
if (v<10)
    fprintf('Velocity reached a max of %.1f at last time of %.2f\n',v,t);
else
    fprintf('Velocity exceeds 10 ft/sec at time=%.2f\n',t);
end
return