Plotting a two dimensional equation with an integral

Hi!

I would like to plot the function

For different values of K. How do I do this?

Thanks in advance

[Tayyab Khalil]

This is what i have come up with, i have taen out the k in the exponent out of the integration as well because for some reason that wasn't working inside, shouldn't have any effect on the end result really. And i assumed that you are working with a fixed value of r.

r = 10; k = -3:0.1:3;
fun = @(x) cos(x).^2.*exp(-0.5*(r*sin(x)).^2)/sqrt(2*pi);
I = k.*exp(-k.^2).*integral(fun, -pi/2, pi/2)
plot(k, I);

[Alan Stevens]

@Tayyab: Note that

exp(-k.^2).*exp(-0.5*(r*sin(x)).^2) = exp(-k.^2-0.5*(r*sin(x)).^2)

not

exp(-0.5*(k*r*sin(x)).^2)

Answer 1

[Alan Stevens]

Something like this

K = 1:10;  % or whatever values you want
for i = 1:numel(K)
    I(i) = integral(@(theta) Ifn(theta,K(i)),-pi/2,pi/2);
end

plot(K,I),grid

function kern = Ifn(theta,K)
         r = 2;   % replace with true value
         kern = cos(theta).^2.*exp(-(K*r*sin(theta)).^2/2)/(2*pi);
end