Find: Use trigonometric substitution to compute the following integral. \int...
Question:
Use trigonometric substitution to compute the following integral.
{eq}\displaystyle \int \frac{x^2}{\sqrt{9-x^2}} {/eq}
Trigonometric Substitution:
For integrals containing square root of quadratic expressions, applying trigonometric substitution is often the most convenient technique in evaluating. In applying this methods, some trigonometric identities may also be needed in simplification steps.
Answer and Explanation: 1
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View this answerLet's apply trigonometric substitution with {eq}\displaystyle x = 3 \sin u {/eq} and {eq}\displaystyle dx = 3 \cos u \,du {/eq} :
{eq}\displayst...
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Chapter 13 / Lesson 12Trigonometric substitutions can be useful by plugging in a function of a variable, thus simplifying the calculation of an integral. Learn how to solve integrals using substitution, tables, by parts, and Riemann Sums through a variety of examples.