Evaluate the following definite integrals: _ 4 ^ 9 1 x dx - Vidyadip

Question

Evaluate the following definite integrals:
$\int_{4}\limits^{9}\frac{1}{\sqrt{\text{x}}} \text{ dx}$

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Answer

Let $\text{I}=\int_{4}\limits^{9}\frac{1}{\sqrt{\text{x}}} \text{ dx}$ Then,
$\text{I}=2\int_{4}\limits^{9}\frac{1}{2\sqrt{\text{x}}} \text{ dx}$
$\Rightarrow\text{I}=2\big[\sqrt{\text{x}}\big]^9_4$
$\Rightarrow\text{I}=2(3-2)$
$\Rightarrow\text{I}=2$

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