## Problem Statement

Calculate the area of the figure bounded by the graphs of the functions:

$$
y=x \sqrt{9-x^{2}}, y=0, (0 \leq x \leq 3)
$$
## Solution

![](https://cdn.mathpix.com/cropped/2024_05_22_aa6951b1e92815ea34b6g-03.jpg?height=557&width=546&top_left_y=961&top_left_x=104)

$$
\begin{aligned}
& S=\int_{0}^{3}\left(x \sqrt{9-x^{2}}\right) d x= \\
& =-\frac{1}{2} \int_{0}^{3}\left(9-x^{2}\right)^{\frac{1}{2}} d\left(9-x^{2}\right)= \\
& =-\left.\frac{1}{2} \cdot \frac{2}{3}\left(9-x^{2}\right)^{\frac{3}{2}}\right|_{0} ^{3}= \\
& =-\frac{1}{3} \cdot(0-27)=9
\end{aligned}
$$

--kasper 11:41, 23 May 2010 (UTC)

Source — «http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\� \%D0\%9A\%D1\%83\%D0\%B7\%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B}+14-2$ »

Categories: Kuznetsov Problem Book Integrals Problem 14 | Integrals

- Last edited: 05:33, 9 June 2010.
- Content is available under CC-BY-SA 3.0.

Created by GeeTeatoo

## Problem Kuznetsov Integrals 14-3

## Material from PlusPi