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Evaluate the integral using the indicated trigonometric substitution. integral 3x^3 sqrt(9-x^2)...

Question:

Evaluate the integral using the indicated trigonometric substitution.

{eq}\displaystyle \int 3x^3 \sqrt{9-x^2}\ dx,\ \ x = 3\ sin(\theta) {/eq}

Indefinite Integral in Calculus:

The integration procedure is used to find out the anti-derivative of different types of functions. Sometimes we need to substitute the given variable by a trigonometric function, this process is called trigonometric substitution.

We can simplify or solve any mathematical problems with trigonometric functions by using trigonometric identities.

Answer and Explanation: 1

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We are given:

$$\displaystyle \int 3x^{3}\sqrt{9 - x^{2}}dx $$

Substitute {eq}x = 3 \sin \theta \rightarrow \ dx = 3 \cos \theta \ d...

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Indefinite Integrals as Anti Derivatives

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Chapter 12 / Lesson 11
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Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.


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