## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 22

Diverges

#### Work Step by Step

\begin{aligned} \int_{1}^{2} \frac{d x}{(x-1)^{2}} &=\lim _{R \rightarrow 1} \int_{R}^{2} \frac{d x}{(x-1)^{2}} \\ &=\lim _{R \rightarrow 1}\left.\frac{(x-1)^{-1}}{(-1)}\right|_{R} ^{2} \\ &=\lim _{R \rightarrow 1}\frac{1}{(R-1)}-1 \\ &=\infty\end{aligned} The integral diverges.

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