Hello! I should determine the values of the following integrals without really calculating:

(1) $\displaystyle \int \limits_{B(2, \pi)}^{} \exp(x) \cdot \cos(y) dx dy$

(2) $\displaystyle \int \limits_{\partial B(x_0, \epsilon)}^{} \log(|x|) dS(x)$, with $\displaystyle 0<\epsilon<|x_0|, x_0 \in \mathbb{R}^2$.

I do not have any clue how to solve this exercise. How can one see the values of these integrals?

Can somebody please help me?