Evaluate the following integral: 1 a^2-b^2x^2 dx - Vidyadip

Question

Evaluate the following integral:
$\int\frac{1}{\sqrt{\text{a}^2-\text{b}^2\text{x}^2}}\text{ dx}$

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Answer

$\int\frac{1}{\sqrt{\text{a}^2-\text{b}^2\text{x}^2}}\text{ dx}$
$=\int\frac{\text{dx}}{\sqrt{\text{b}^2\Big(\frac{\text{a}^2}{\text{b}^2}-\text{x}^2}\Big)}$
$=\frac{1}{\text{b}}\int\frac{\text{dx}}{\sqrt{\big(\frac{\text{a}}{\text{b}}\big)^2-\text{x}^2}}$
$=\frac{1}{\text{b}}\sin^{-1}\Big(\frac{\text{xb}}{\text{a}}\Big)+\text{C}$

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