{"id":48,"date":"2021-03-25T02:20:44","date_gmt":"2021-03-25T02:20:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/trigonometric-substitution\/"},"modified":"2021-11-17T02:25:15","modified_gmt":"2021-11-17T02:25:15","slug":"trigonometric-substitution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/trigonometric-substitution\/","title":{"raw":"Introduction to Trigonometric Substitution","rendered":"Introduction to Trigonometric Substitution"},"content":{"raw":"

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<\/span> comes in very handy when evaluating these integrals. This technique uses substitution to rewrite these integrals as trigonometric integrals.<\/p>","rendered":"

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<\/span> comes in very handy when evaluating these integrals. This technique uses substitution to rewrite these integrals as trigonometric integrals.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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