Evaluate: ^3_23^x dx - Vidyadip

Question

Evaluate:
$\int\limits^3_23^\text{x}\text{ dx}$

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Answer

$\text{I}=\int\limits^3_23^\text{x}$
$=\Big[\frac{3\text{x}}{\log3}\Big]^3_2+\text{C}$ $\Big(\text{Use}:\int\text{a}^{\text{x}}=\frac{\text{a}^{\text{x}}}{\log\text{a}}+\text{C}\Big)$
$=\frac{3^3}{\log3}-\frac{3^2}{\log3}+\text{C}$
$=\frac{1}{\log3}(3^2-3^3)+\text{C}$
$=\frac{1}{\log3}(27-9)+\text{C}$
$=\frac{1}{\log3}(18)+\text{C}$

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