What is the integral of pi(2x)^2 ?

The integral of pi(2x)^2 is (4pix^3)/3+C

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integral of pi(2x)^2

\int π (2 x)^{2} d x

\frac{4 π x ^{3}}{3} + C

Solution steps

\int π (2 x)^{2} d x

Take the constant out:

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

= π \cdot \int (2 x)^{2} d x

Simplify

(2 x)^{2} : 4 x^{2}

= π \cdot \int 4 x^{2} d x

Take the constant out:

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

= π 4 \cdot \int x^{2} d x

Apply the Power Rule

= π 4 \cdot \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{4 π x ^{3}}{3}

Add a constant to the solution

= \frac{4 π x ^{3}}{3} + C