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10 lis 2020 · Learning Objectives. Solve integration problems involving the square root of a sum or difference of two squares. In this section, we explore integrals containing expressions of the form \ (\sqrt {a^2−x^2}\), \ (\sqrt {a^2+x^2}\), and \ (\sqrt {x^2−a^2}\), where the values of \ (a\) are positive.
In mathematics, a trigonometric substitution replaces a trigonometric function for another expression. In calculus, trigonometric substitutions are a technique for evaluating integrals. In this case, an expression involving a radical function is replaced with a trigonometric one.
16 paź 2023 · Learn how to use trig substitutions to integrate expressions with roots, such as √a2x2 − b2 or √a2 + b2x2. See the general forms, the substitutions, the limits and the differentials for each case.
This calculus video tutorial provides a basic introduction into trigonometric substitution. It explains when to substitute x with sin, cos, or sec.
Khan Academy
21 gru 2020 · Given a definite integral that can be evaluated using Trigonometric Substitution, we could first evaluate the corresponding indefinite integral (by changing from an integral in terms of \(x\) to one in terms of \(\theta\), then converting back to \(x\)) and then evaluate using the original bounds.
Overview. This technique is useful for integrating square roots of sums of squares. This session also covers the trigonometry needed to convert your answer to a more useful form. Lecture Video and Notes. Video Excerpts. Clip 1: Example of Trig Substitution. Clip 2: Undoing Trig Substitution. Clip 3: Summary of Trig Substitution. Worked Example.
