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

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

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

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Answer

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

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

Main topic:

Integration by trigonometric substitution

Used formulas:

4. See formulas

Time to solve it:

~ 7.16 seconds