(1 point) Find area of the region under the curve $y=6-x^{2}$ and above the $x$-axis. \[ \text { area }= \]

Step 1 ：To find the area under the curve \(y=6-x^2\) and above the x-axis, we need to integrate the function with respect to \(x\).

Step 2 ：We find the points of intersection with the x-axis by setting \(y=0\) and solving for \(x\), which gives us \(-\sqrt{6}\) and \(\sqrt{6}\).

Step 3 ：The area is then the integral of \(6-x^2\) from \(-\sqrt{6}\) to \(\sqrt{6}\).

Step 4 ：Calculating the integral, we get the area as \(8\sqrt{6}\).

Step 5 ：The final answer is \(\boxed{8\sqrt{6}}\).