# 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.

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