MATLAB: How to integrate this function in the photo on matlab pls help

integration.rho

Best Answer

Integrate with respect to what?

The del operator together with the magnitude operator imply that rho is not a scalar but is instead a function. You are not going to have any success integrating F[rho] without naming a particular rho.

syms rho(x,y) R T alpha beta kappa real
F = rho*R*T*log(rho/(1-beta*rho)) - alpha*rho^2 + kappa/2 * (diff(rho,x).^2 + diff(rho,y).^2)

but integrating F with respect to x or y will not go anywhere without a particular rho.

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MATLAB: Double integral of a dot product error

integral2() assumes that the function handle is able to accept matrix inputs. However, the fun() function in your code does not work correctly with matrix inputs. The following codes shows a quick fix using arrayfun

light_dir = [-0.6626;0;-0.7490];
camera_dir = [-1;0;0];
R = sqrt(2/(4*pi));
x_c =@(theta,phi) R.*sin(theta).*cos(phi);
y_c =@(theta,phi) R.*sin(theta).*sin(phi);
z_c =@(theta) R.*cos(theta);
normal =@(theta,phi) [x_c(theta,phi); y_c(theta,phi); z_c(theta)];
fun = @(theta,phi) (dot(light_dir,normal(theta,phi))).*(dot(camera_dir,normal(theta,phi))<0).*R^2.*sin(theta);
intensity = integral2(@(THETA, PHI) arrayfun(@(theta,phi) fun(theta, phi), THETA, PHI) ,0,pi,0,2*pi);

MATLAB: Problems with an integral

alpha1 = 1.8;
kappa1 = 25;
alpha2 = 2.2;
kappa2 = 27;
syms x z; 
f = alpha1 * alpha2 * kappa1 * kappa2 * (x-z)^(kappa1-1) * x^(kappa2-1)*exp(-alpha1*(x-z)^kappa1-alpha2*(x^kappa2-(x-z)^kappa2)); 
I = int(f,z,[0 inf]);
fVpa = vpa(I)

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Related Solutions

MATLAB: Double integral of a dot product error

MATLAB: Problems with an integral

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