## Problem Set: Integrals Resulting in Inverse Trigonometric

In the following exercises (1-6), evaluate each integral in terms of an inverse trigonometric function.

1. ${\displaystyle\int }_{0}^{\sqrt{3}\text{/}2}\frac{dx}{\sqrt{1-{x}^{2}}}$

2. ${\displaystyle\int }_{-1\text{/}2}^{1\text{/}2}\frac{dx}{\sqrt{1-{x}^{2}}}$

3. ${\displaystyle\int }_{\sqrt{3}}^{1}\frac{dx}{\sqrt{1+{x}^{2}}}$

4. ${\displaystyle\int }_{1\text{/}\sqrt{3}}^{\sqrt{3}}\frac{dx}{1+{x}^{2}}$

5. ${\displaystyle\int }_{1}^{\sqrt{2}}\frac{dx}{|x|\sqrt{{x}^{2}-1}}$

6. ${\displaystyle\int }_{1}^{2\text{/}\sqrt{3}}\frac{dx}{|x|\sqrt{{x}^{2}-1}}$