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

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

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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{r ^{4}}{4}

= \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

\frac{d}{d x} ((x + 1)^{3} - x^{3})

\int_{2}^{4} \frac{2}{x ^{2} - 6 x + 10} d x

(- 2.1) (4.2)

f (x) = (x^{2} + 7) (5 - x), at x = 0

\frac{d}{d x} (x^{4} + (y - 2)^{3})