Description
This lesson covers the two types of trigonometric integrals. The first type features integrands that contain one or more trig functions. Evaluating these often involves manipulating the integrand using the trig identities in order to get it into an integrable format. I provide ten examples, covering all the techniques that students are likely to run into in these types of problems. The second type features integrals with square roots whose radicands are in the form a^2 - x^2, a^2 + x^2, or x^2-a^2, in which we use aspects of right triangles to manipulate the integrand into something integrable. I provide four examples, covering all the techniques that students a likely to run into in these types of problems. The last example is a two-page problem that involves completing the square in order to turn the integrand into the second type of trig integral.
The document includes definitions, techniques, and thorough explanations to go along with the worked examples.
Highlights
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Description
This lesson covers the two types of trigonometric integrals. The first type features integrands that contain one or more trig functions. Evaluating these often involves manipulating the integrand using the trig identities in order to get it into an integrable format. I provide ten examples, covering all the techniques that students are likely to run into in these types of problems. The second type features integrals with square roots whose radicands are in the form a^2 - x^2, a^2 + x^2, or x^2-a^2, in which we use aspects of right triangles to manipulate the integrand into something integrable. I provide four examples, covering all the techniques that students a likely to run into in these types of problems. The last example is a two-page problem that involves completing the square in order to turn the integrand into the second type of trig integral.
The document includes definitions, techniques, and thorough explanations to go along with the worked examples.
