Find the resonance of waves if the function that describe the wave length is f(x)f(x)=sinxcosx

To study the resonance of waves, we'll just have to
calculate the indefinite integral of the given
function:

f(x) =
(sinx)*(cosx)

Int (sinx)*(cosx)
dx

We'll use substitution
technique:

sin x = t

We'll 
differentiate:

cos x dx =
dt

We'll re-write the function in the variable
t:

Int t dt = t^2/2 + C

But t
= sin x, so

The system is in resonance if and only
if:

Int (sinx)*(cosx) dx = (sinx)^2/2 +
C