Question

Express the signed area between the graph of $y=\frac{1}{x}$ and the x-axis from $x=e$to $x=10$in terms of logarithms.

Short answer

The signed area between the graph of $y=\frac{1}{x}$ and the x-axis from $x=e$to $x=10$ is $\ln 10-1$.

Step-by-step solution

Step 1. Given Information.

The graph of the function:

$y=\frac{1}{x}$

The function is from $x=etox=10$.

Step 2. Find the signed area.

The signed are is given by,

$$\begin{gathered} {\int }_e^{10}\frac{1}{x}dx={[\ln x]}_e^{10} \\ =\ln 10-\ln e \\ =\ln 10-1 \end{gathered}$$