How can we calculate the following integral? $ \int_{0}^r\frac{1}{s^n}\int_{B(s)}f(x)dxds $ Here $B(s)$ is the ball of radius $s$ centered at the origin.
I think that this can be computed by $ \int_{0}^r\frac{1}{s^n}\int_{B(s)}f(x)dxds =\int_{0}^r\frac{1}{s^n}\int_{0}^s\int_{\partial B(t)}f(x)dxdsdt $ But I am stuck at this point. Any help is more than welcome.