"Use properties of the integral and the formulas..." was answered by our experts

Secondary
Calculus and Analysis
Calculus 2
Applications of integrals

eozoischgc Answered2022-01-02

Use properties of the integral and the formulas in the summary to calculate the integrals.

\int_{0}^{9} x^{2} d x

Answer & Explanation

Wendy Boykin

Expert

2022-01-03Added 35 answers

Step 1
The given integral is

\int_{0}^{9} x^{2} d x

.
Step 2
Use the formula

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

\int_{0}^{9} x^{2} d x = {[\frac{x^{2 + 1}}{2 + 1}]}_{0}^{9}

= \frac{1}{3} (9^{3} - 0^{3})

= \frac{729}{3}

=243
Hence, the value of the integral

\int_{0}^{9} x^{2} d x

is 243.

vrangett

Expert

2022-01-04Added 36 answers

Step 1
Given:

\int x^{2} d x

\int x^{2} d x = \frac{x^{3}}{3}

Step 2
Lets

Vasquez

Expert

2022-01-07Added 457 answers

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

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