View Policies Current Attempt in Progress Find the area of the region under $y=11 \ln (4 x)$ and above $y=6$ for $4 \leq x \leq 8$. Round your answer to three decimal places. Area $=\mathbf{i}$ i . eTextbook and Media Save for Later

Step 1 ：The area under the curve $y = 11 \ln(4x)$ and above the line $y = 6$ from $x = 4$ to $x = 8$ can be found by integrating the function $f(x) = 11 \ln(4x) - 6$ from $4$ to $8$. This is because the integral of a function gives the area under the curve of that function. We subtract $6$ because we want the area above the line $y = 6$.

Step 2 ：Calculate the integral to find the area.

Step 3 ：The calculated area is 114.991.

Step 4 ：Final Answer: The area of the region under $y=11 \ln (4 x)$ and above $y=6$ for $4 \leq x \leq 8$ is \(\boxed{114.991}\).