_4^9 1 x d x= - Vidyadip

MCQ

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

A
1
B
-2
C
2
D
-1

✓

Answer

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

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