Evaluate the definite integral in Exercise: _ 2 ^ 3 1 x dx - Vidyadip

Question

Evaluate the definite integral in Exercise:
$\int_{2}^{3}\frac{1}{\text{x}}\text{dx}$

✓

Answer

$\text{Let} \ \text{I}=\int\limits_{2}^{3}\frac{1}{\text{x}}\ \text{dx}$

$\int\frac{1}{\text{x}}\text{dx}=\text{log}|\text{x|}=\text{F}\text{(x)}$

By second fundamental theorem of calculus, we obtain

$\text{I}=\text{F}(3)-\text{F}(2)$

$=\text{log|3|}-\text{log|2|}=\text{log}\frac{3}{2}$

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