eozoischgc

2022-01-02

Use properties of the integral and the formulas in the summary to calculate the integrals.
${\int }_{0}^{9}{x}^{2}dx$

Wendy Boykin

Expert

Step 1
The given integral is ${\int }_{0}^{9}{x}^{2}dx$.
Step 2
Use the formula $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$.
${\int }_{0}^{9}{x}^{2}dx={\left[\frac{{x}^{2+1}}{2+1}\right]}_{0}^{9}$
$=\frac{1}{3}\left({9}^{3}-{0}^{3}\right)$
$=\frac{729}{3}$
=243
Hence, the value of the integral ${\int }_{0}^{9}{x}^{2}dx$ is 243.

vrangett

Expert

Step 1
Given:
$\int {x}^{2}dx$
$\int {x}^{2}dx=\frac{{x}^{3}}{3}$
Step 2
Lets

Vasquez

Expert

${\int }_{0}^{9}{x}^{2}dx$
$\int {x}^{2}dx$
$\frac{{x}^{3}}{3}$
Return the limits
$\frac{{x}^{3}}{3}{|}_{0}^{9}$
Calculate
$\frac{{9}^{3}}{3}-\frac{{0}^{3}}{3}$
Solution
243

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