Interpolate function using Spline and Lagrange interpolation and take definite integral from it

I have the function f(x) = 1 - exp(-x); xk = 0.3*k; k = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]; integral from 0 to 3; I have found how take integral from f(x), spline function. I have not found lagrange function. How i can take integral from spline function and how i can interpolate with lagrange and then take integral from it.

when i take integral from spline i have this message in command windows

Error using integralCalc/finalInputChecks (line 522)

Input function must return 'double' or 'single' values. Found 'struct'.

Error in integralCalc/iterateScalarValued (line 315)

finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

Error in lab1 (line 19)

clc;
clear;
k = [0 1 2 3 4 5 6 7 8 9 10];
xpoints = 0.3 * k;
ypoints = 1 - exp(-xpoints);

%f(x) function and integral
f = @(x) 1 - exp(-x);
fplot(f, [0 3.0]);
grid on;
integralFx = integral(f, 0, 3);
fprintf("%f\n", integralFx);

%s(x)

f(xpoints);
s = @(x) spline(xpoints, ypoints);
integral (s, 0, 3);

Answer 1

[John D'Errico]

I'm not at all sure

f(xpoints);
s = @(x) spline(xpoints, ypoints);
integral (s, 0, 3);

what you think the line f(xpoints); does? All it does is evaluate the function f at the vector xpoints, then it dumps the result into the bit bucket, never to be seen again.

Next, the line where you create s? It does not create a function you can evaluate. You can do that as:

s = spline(xpoints,ypoints);
S = @(x) ppval(s,x);
integralSx = integral(S, 0, 3)

integralSx =
           2.0497680394453

[Valery Kvan]

thx, i think that is what i need because results is close with other programms results. Try to find function for lagrange interpolation and take integral from lagrange polynom by myself.

[John D'Errico]

You were close. Now you need to write a function that does Lagrange interpolation. Use integral the same way.

Thus if I call the function S at a list of points,

S([.1 2.3])
ans =
        0.0949948404628685         0.899741790030172

it gives me a result, just as if I had called the function f.

So you need to write that Lagrange interpolation function.