X=-2:0.1:6;
y=0.4;
t=0.75;
v=1.5;
alpha=0.1;
for i=1:numel(X)
x = X(i);
Fun = @(r)fun(r,x,y,t,v,alpha);
C(i) = integral(Fun,0,Inf);
end
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 5.9e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 6.5e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 6.7e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 7.1e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 7.4e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 8.1e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 8.3e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 9.4e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 9.7e-09. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.0e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.1e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.2e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.2e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.3e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.4e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.6e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.6e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.7e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.9e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.0e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.2e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.3e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.4e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.6e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.8e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 3.0e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 3.2e-08. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.
plot(X,C)
function value = fun(r,x,y,t,v,alpha)
gamma=1/(1-alpha);
A=exp(v/2*(x+y)-alpha*gamma*t);
B=(r.^3)./(r.^2+gamma+v^2/2).^2;
D=exp((alpha*gamma.^2*t)./(r.^2+gamma+v^2/2));
K=besselj(0,r.*sqrt(x.^2+y.^2));
L=besselj(2,r.*sqrt(x.^2+y.^2));
M=B.*D.*(K+L);
value = alpha*gamma^2*y*A*M;
end
