# Surface Integral - Mean Value Property

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

• It seems to me that there are too many x's in your notes - it should be u(y) dS(y) in the integrand. Hence A is u(a) times some volume element (check the definition of the integral!). – Stockfish Oct 15 '18 at 19:29