How can I solve the following integral equation

How can I solve the following integral equation in MATLAB numerically:

where:

Answer 1

[Ameer Hamza]

Try this

A = @(t) t.^2; % equation of A w.r.t. t. A(t) = t^2 for example
% f as function of t and w
f = @(t,w) A(t).*cos(w.*t) + integral(@(tau) w.*A(tau).*sin(w.*tau), 0, t);

Evaluate it like this

t = 10;
w = 2;
y = f(t,w);

>> y
y =
    8.8335

[parham kianian]

Function A(t) is unknown not f(t). I need to evaluate A(t).

[Ameer Hamza]

Can you share the expression for f(t)?