(1 point)

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

Answer

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Answer

The final answer is $\boxed{8\sqrt{6}}$.

Steps

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 $\boxed{8\sqrt{6}}$.