_4^9 1 x d x - Vidyadip

Question

$\int_4^9 \frac{1}{\sqrt{x}} d x$

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Answer

$
\begin{aligned}
& \text { Let } I =\int_4^9 \frac{1}{\sqrt{x}} \cdot d x \\
& =\int_4^9 x^{\frac{1}{2}} \cdot d x=\left[\frac{x^{\frac{1}{2}}}{\frac{1}{2}}\right]_4^9 \\
& =2[\sqrt{x}]_4^9 \\
& =2(\sqrt{9}-\sqrt{4}) \\
& =2(3-2) \\
& \therefore I =2 .
\end{aligned}
$

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