Trigonometric Substitution (Calculus 2)

What is trigonometric substitution? The simple answer: it's a technique for integrating functions that contain square roots or radicals. We go through everything that you need to know for this technique: the 3 substitutions and why we use them, the necessary Pythagorean identities, the work for plugging these substitutions in and getting the square roots to cancel, how to substitute back in terms of x using a conversion triangle, and the differentials for these substitutions. Problems are linked below.

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► Artist Attribution
Music By: "After The Fall"
Track Name: "Pieces"
Music Published by: Chill Out Records LLC
License: Creative Commons Attribution 4.0 International (CC BY - 4.0)

[melissabowers]

If you remember the right triangles and derive the values from there, the substitution makes more sense. You have to draw those triangles anyways to convert thetas back to x's at the end anyways. The conversion triangle can help jog your memory should you forget whether to use tan, sec,