# Integral of x^2(9-1x^2)^0.5

## Answer

$\int81\sin\left(\theta\right)^2\cos\left(\theta\right)^2d\theta$

## Step-by-step explanation

Problem

$\intx^2\sqrt{9-x^2}dx$

1

Solve the integral $\int\sqrt{9-x^2}x^2dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=3\sin\left(\theta\right) \\ dx=3\cos\left(\theta\right)d\theta\end{matrix}$

## Answer

$\int81\sin\left(\theta\right)^2\cos\left(\theta\right)^2d\theta$