Find the area between the curve and the $x$-axis over the indicated interval
\[
y=\frac{3}{x} ;[1,6]
\]
The area under the curve is (Type an exact answer.)
Answer
Final Answer: The area under the curve is \(\boxed{3*\log(6)}\).
Step 1 ：The problem is to find the area between the curve and the x-axis over the interval [1,6] for the function \(y=\frac{3}{x}\).
Step 2 ：The area under a curve from a to b is given by the definite integral from a to b of the function.
Step 3 ：In this case, the function is \(y=\frac{3}{x}\) and the interval is [1,6]. So, we need to calculate the definite integral of \(\frac{3}{x}\) from 1 to 6.
Step 4 ：The area under the curve \(y=\frac{3}{x}\) from \(x=1\) to \(x=6\) is \(3*\log(6)\).
Step 5 ：Final Answer: The area under the curve is \(\boxed{3*\log(6)}\).
