Introduction to Trigonometric Substitution

In this section, we explore integrals containing expressions of the form [latex]\sqrt{{a}^{2}-{x}^{2}}[/latex], [latex]\sqrt{{a}^{2}+{x}^{2}}[/latex], and [latex]\sqrt{{x}^{2}-{a}^{2}}[/latex], where the values of [latex]a[/latex] are positive. We have already encountered and evaluated integrals containing some expressions of this type, but many still remain inaccessible. The technique of trigonometric substitution comes in very handy when evaluating these integrals. This technique uses substitution to rewrite these integrals as trigonometric integrals.