Evaluate the following integral for \( z \in \mathbb{C}^+ \).
\[
\frac{1}{2\pi} \int_{-2}^2 \log (z-x) \sqrt{4-x^2} dx.
\]
KAIST Math Problem of the Week
Weekly Math Challenges in KAIST
Evaluate the following integral for \( z \in \mathbb{C}^+ \).
\[
\frac{1}{2\pi} \int_{-2}^2 \log (z-x) \sqrt{4-x^2} dx.
\]
what does C^{+} mean?
Set of all complex numbers with positive imaginary part.
Is (4-x^{2})^{1/2} outside the log or not?
It is outside the log. (Otherwise, there would have been parentheses.)