Compute the area of the region under the graph of $f (x) = \frac{8}{x}$ from $x = 6$ to $x = 12$ .
$Area =$
Submit Answer

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $- 8 \log (6) + 8 \log (12)$

Steps

Step 1 ：Calculate the definite integral of the function $f (x) = \frac{8}{x}$ from $x = 6$ to $x = 12$

Step 2 ：Use the formula for the definite integral of $f (x) = \frac{8}{x}$ to find the area under the curve

Step 3 ：Compute the integral to get $- 8 \log (6) + 8 \log (12)$

Step 4 ：Simplify the expression using logarithm properties

Step 5 ：Final Answer: $- 8 \log (6) + 8 \log (12)$