Mathematics

Problem

The function

g

is defined on

[-3,3]

by the equation

g(x)=\sqrt{9-x^{2}}

, the upper half of a circle of radius 3 centered at the origin. Determine whether the value of

\displaystyle\int_{-3}^{3} g(x)\,dx

is positive, negative, or zero, and justify your answer in one sentence.