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

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

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integral of 4/3 pix^3

\int \frac{4}{3} π x^{3} d x

\frac{π x ^{4}}{3} + C

Solution steps

\int \frac{4}{3} π x^{3} d x

Take the constant out:

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

= \frac{4}{3} π \cdot \int x^{3} d x

Multiply fractions:

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

= \frac{4 π}{3} \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

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

Simplify

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

= \frac{π x ^{4}}{3}

Add a constant to the solution

= \frac{π x ^{4}}{3} + C

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