Integral calculation using matlab

Hello i wish to calculate the following integral

My difficulty stems from the absolute value which is "outside" of the integral with respect to θ

Answer 1

[Bruno Luong]

Feel free to change these hyper-parameters

n = 3
k = 2*pi*rand()

integral(@(phi) arrayfun(@(phi) abs(integral(@(theta) exp(1i*k*cos(theta-phi)).*cos(n*theta), 0, 2*pi)).^2, phi), 0, 2*pi)

[MINAS KOUROUMPLAKIS]

Thank you for your reply, i get this error message

Error using subsindex

Function 'subsindex' is not defined for values of class 'function_handle'.

Error in sym/subsref (line 771)

R_tilde = builtin('subsref',L_tilde,Idx);

[Bruno Luong]

I proposed numerical method, not symbolic. You enter n and k as double numbers then it will work fine.

Can't hep you if you want symbolic integration; someone else might help you because I don't own symbolic tbx.

[Matt J]

Looks like a square .^2 is missing from the absolute value.

[Bruno Luong]

Oh heah, thank you for spotting the error Matt. I'll fix it.

Answer 2

[Matt J]

My difficulty stems from the absolute value which is "outside" of the integral

Why is this a difficulty? Because it prevents you from using integral2()? Just apply integral() twice instead.

[MINAS KOUROUMPLAKIS]

Can you please elaborate, i am ashamed to say that i don't see how i can do it without integral2()?

[MINAS KOUROUMPLAKIS]

Tried everything, nothing!

[Matt J]

Use integral() to evaluate the inner integral (over theta). Then take the absolute value squared of that. Then apply integral() again to integrate the result fo the previous step over phi.

[MINAS KOUROUMPLAKIS]

This is what i do and i get an error message

fun=@(x,y)exp(-1i*cos(x-y)).*cos(x)

fun = @(x,y)exp(-1i*cos(x-y)).*cos(x)

>> integral(@(x) f(x,y),0,2*pi)

Error using subsindex

Function 'subsindex' is not defined for values of class 'function_handle'.

Error in sym/subsref (line 771)

R_tilde = builtin('subsref',L_tilde,Idx);

[Steven Lord]

Write a function to compute the inner integral. This function should accept phi. One wrinkle here is that since the outer integral call is going to pass a vector of values into it as phi, your inner integral call will need to say that the function is ArrayValued.

Write a function that takes the absolute value of that inner integral function.

Write a function to compute the outer integral of the absolute value function.

If you try this and it doesn't work, show us the code you wrote and we may be able to offer some guidance.