I have been given this question to solve however I'm having some difficulty solving it as I am quite new to Partial Differential Equations:
Let $ a = (2,2) $ and $ r =5 $
Compute the following surface integral
$$ A := \int_{\partial{B}(a,r)}\frac{x}{x^2+y^2}{dS}$$
I have been given the hint: try to use the mean value formula rather than computing the actual surface integral.
I have the mean value formula in my notes as:
$$ u(x) = {\int\!\!\!\!\!\!-}_{B(x,r)}u(y)dy = {\int\!\!\!\!\!\!-}_{\partial B(x,r)}u(y)dS(y)$$
However I'm struggling to apply this formula to the given function in the question