"A particle of mass m executes one-dimensional simple harmonic oscillation
under the action of a conservative force such that its instantaneous x coordinate
is x(t) = a cos(ωt − φ).
Find the average values of x, x^2, x', and (x')2 over a single cycle of the oscillation.
Find the average values of the kinetic and potential energies of the
particle over a single cycle of the oscillation."
Average value of a function = integral of a function / interval of the integral
The Attempt at a Solution
So I just want to make sure I can set the integral up like this:
integral from 0 to 2π (A cos(θ)) dθ
basically is it alright to convert A cos(wt - phi) ----> A cos (θ)