What is the integral of 4/3 pir^3 ?

The integral of 4/3 pir^3 is (pir^4)/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 4/3 pir^3

\int \frac{4}{3} π r^{3} d r

\frac{π r ^{4}}{3} + C

Solution steps

\int \frac{4}{3} π r^{3} d r

Take the constant out:

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

= \frac{4}{3} π \cdot \int r^{3} d r

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 π}{3} \cdot \int r^{3} d r

Apply the Power Rule

= \frac{4 π}{3} \cdot \frac{r ^{4}}{4}

Simplify

\frac{4 π}{3} \cdot \frac{r ^{4}}{4} : \frac{π r ^{4}}{3}

= \frac{π r ^{4}}{3}

Add a constant to the solution

= \frac{π r ^{4}}{3} + C