Numerical Integration on Matlab

There are 4 integrals I need to write, but I can't get correct results from them. Did I write it right?

Equations that end in c are constants. they don't change

xi_0 = r(1)/Rprop;

xi_1 = 1;

I1_c = 4*G*(1-epsilon*tan(phi));

I1 = integral(@(xint) xint*I1_c, xi_0, xi_1);

I2_c = lambda*(1+epsilon/tan(phi))*sin(phi)*cos(phi);

I2 = integral(@(xint) ((xint*I1_c)/2.*xint),xi_0,xi_1);

J1_c = 4*G*(1+epsilon/tan(phi));

J1 = integral(@(xint) xint*J1_c ,xi_0, xi_1);

J2_c = (1-epsilon*tan(phi))*((1+cos(2*phi))/(2));

J2 = integral(@(xint) (xint*J1_c)/2 ,xi_0,xi_1);

Answer 1

[Riccardo Scorretti]

Hi. I would say no: you forget to multiply I2 and J2 by the respective constants I2_c and J2_c. That being said, these functions are polynomials with respect to xi: at your place I would go analytically.

Answer 2

[Torsten]

I2 = integral(@(xint) ((xint*I1_c*I2_c)/2.*xint),xi_0,xi_1);
J2_c = (1-epsilon*tan(phi))*(cos(phi))^2;
J2 = integral(@(xint)  (xint*J1_c)/2*J2_c ,xi_0,xi_1);

Not sure whether

I2' = lambda*(I1'/2 * zeta ...

or

I2' = lambda*(I1'/(2*zeta) ...

Some authors write

1/2*zeta

and mean

1/(2*zeta)