Error in using 'cumtrapz' for integration

Hello

I need to use 'cumtrapz' for a particular part of my project, but before that i am trying to understand how it works for multiple time cumulative integration. As a test, i was trying the following basic code:

ny = 101;                                                                  
eta = linspace(-1,1,ny)'; 
f1 = sin(eta);

% Calculation of first cumulative integral
g1 = cumtrapz(eta,f1);

% Calculation of second cumulative integral
h1 = cumtrapz(eta,g1);

% Calculation of third cumulative intergal
k1 = cumtrapz(eta,h1);

We know that first integration of sinx is -cosx and then second intergration is -sinx.

So the value of g1 at each grid point must match {-cos(grid point) + cos(-1)}, Which it does.

But then the value of h1 at each grid point must match {-sin(grid point) + sin(-1)}, which it doesn't.

I was wondering why this happens.

Answer 1

[Matt J]

But next, value of h1 at each grid point must match {-sin(grid point value) - (-sin(-1))},

No, it will be -sin(x)+x*cos(-1) -( -sin(-1)-1*cos(-1))

[N Haq]

Thank you for your response Matt J, could you kindly elaborate why?

[Matt J]

What is the indefinite integral of f(x)=-cos(x)+c? It is g(x)=-sin(x)+c*x.

The definite integral from a to b is therefore,

g(b)-g(a) = (-sin(b)+c*b) - (-sin(a)+c*a)

Now, substitute in b=x and a=-1 and c=cos(-1).

[N Haq]

Thank you Matt ! This really helped , i appreciate your time.