What is the integral from 0 to 3 of x^2(2x)/9 ?

The integral from 0 to 3 of x^2(2x)/9 is 9/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 3 of x^2(2x)/9

\int_{0}^{3} x^{2} \frac{2 x}{9} d x

\frac{9}{2}

Decimal

4.5

Solution steps

\int_{0}^{3} x^{2} \frac{2 x}{9} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{9} \cdot \int_{0}^{3} x^{2} x d x

Simplify

x^{2} x : x^{3}

= \frac{2}{9} \cdot \int_{0}^{3} x^{3} d x

Apply the Power Rule

= \frac{2}{9} [\frac{x ^{4}}{4}]_{0}^{3}

Compute the boundaries:

\frac{81}{4}

= \frac{2}{9} \cdot \frac{81}{4}

Simplify

= \frac{9}{2}

What is the integral from 0 to 3 of x^2(2x)/9 ?
The integral from 0 to 3 of x^2(2x)/9 is 9/2