(1 point) Find area of the region under the curve $y=3 x^{3}-9$ and above the $x$-axis, for $4 \leq x \leq 6$. area $=$

Step 1 ：We are given the function \(y=3x^3-9\) and we are asked to find the area under the curve and above the x-axis, for \(4 \leq x \leq 6\).

Step 2 ：The area under the curve is given by the definite integral of the function from the lower limit to the upper limit.

Step 3 ：So, we need to integrate the function \(y=3x^3-9\) from \(x=4\) to \(x=6\).

Step 4 ：After performing the integration, we find that the area under the curve is 762.

Step 5 ：\(\boxed{762}\) is the final answer.