Chapter 9.4, Problem 52E

To determine

Tofind: the value of the integral.

Answer to Problem 52E

The integral is diverges.

Explanation of Solution

Given information:

Theintegral is ${\displaystyle {\int }_0^1\frac{dx}{x-1}}$ .

Calculation: to find the value of integral, first integrate and then simplify,

  $\begin{array}{l}{\displaystyle {\int }_0^1\frac{dx}{x-1}}={\left[\ln \left(x-1\right)\right]}_0^1\text{ [}{\displaystyle \int \frac{1}{x}}=\ln x]\\ {\displaystyle {\int }_0^1\frac{dx}{x-1}}=\ln \left(1-1\right)-\ln \left(0-1\right)\\ {\displaystyle {\int }_0^1\frac{dx}{x-1}}=\text{not defined [simplify]}\end{array}$

Thus, the integral is diverges.