# Chapter 4 - Integration - Chapter 4 Review Exercises - Page 344: 29

$$\frac{2}{3}$$

#### Work Step by Step

\eqalign{ & \int_1^3 {\frac{1}{{{x^2}}}} dx \cr & {\text{write with negative exponent}} \cr & = \int_1^3 {{x^{ - 2}}} dx \cr & {\text{find the antiderivative by the power rule}} \cr & = \left( {\frac{{{x^{ - 2 + 1}}}}{{ - 2 + 1}}} \right)_1^3 \cr & = \left( {\frac{{{x^{ - 1}}}}{{ - 1}}} \right)_1^3 \cr & = \left( { - \frac{1}{x}} \right)_1^3 \cr & {\text{part 1 of fundamental theorem of calculus}} \cr & = - \frac{1}{3} - \left( { - \frac{1}{1}} \right) \cr & {\text{simplify}} \cr & = - \frac{1}{3} + 1 \cr & = \frac{2}{3} \cr}

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