MATLAB: How to find a double integral

integral2syms

I need to integrate the function wrt theta and phi. How to do it? m,n, p are constants.


f=m*p*cos(theta)^3*sin(phi)^2 - n*p*cos(phi)^2*cos(theta)^3 - m*n*cos(theta)*sin(phi)^2*sin(theta)^2 + m*n*cos(phi)*cos(theta)*sin(phi)*sin(theta)^2

Best Answer

It is best to vectorize your function using element-wise operations, then create it as a function of the two variables, then use integral2 to numerically integrate it:

m = 3;
n = 5;
p = 7;
f = @(theta,phi) m*p*cos(theta).^3.*sin(phi).^2 - n*p*cos(phi).^2.*cos(theta).^3 - m*n*cos(theta).*sin(phi).^2.*sin(theta).^2 + m*n*cos(phi).*cos(theta).*sin(phi).*sin(theta).^2;
f_int = integral2(f, 0, 2*pi, 0, 2*pi)

I created values for the constants to test the code.

Related Solutions

MATLAB: Solving non linear equation using fsolve

You are not passing theta_n and other parameters to root2d(). One fix is to make root2d a Nested Function. Also, you must choose a different initial point. phi0 = [10,10] worked for me.

function solve_it()
    beta_a = 10;
    alpha_n = 10 ;
    eta= 18;
    i = 18;
    theta_i = 10;
    theta_n = 10 ;
    
    fun = @root2d;
    phi0 = [10,10];
    phi = fsolve(fun,phi0);
    phi_n = phi(1),
    phi_i = phi(2),
    function F = root2d(phi)
    F = zeros(2,1);
    F(1) = (pi*sin((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2) - (pi*cos((pi*phi(1))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((phi(1)*pi)/180)^2*(cos((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180) + sin((pi*phi(2))/180)*tan((pi*theta_i)/180)));
    F(2) = ((cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180))*((pi*cos((pi*(phi(1) + theta_n))/180)*sin((pi*phi(2))/180))/180 - (pi*cos((pi*phi(2))/180)*tan((pi*theta_i)/180))/180))/(sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2);
    end
end

MATLAB: How to define a function that evaluates in input

function y=T(theta_Degree)
theta=theta_Degree*pi/180;
y=[cos(theta)^2 sin(theta)^2 2*cos(theta)*sin(theta);sin(theta)^2 cos(theta)^2 -2*cos(theta)*sin(theta);-cos(theta)*sin(theta) cos(theta)*sin(theta) cos(theta)^2-sin(theta)^2];
end

Then type in command line

T(40)

and see the results.

Best Answer

Related Solutions

MATLAB: Solving non linear equation using fsolve

MATLAB: How to define a function that evaluates in input

Related Question