Problem

(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 $=$

Solution

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.

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Source: https://solvelyapp.com/problems/bnboXZQUhA/

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