What is the integral of pi(4x)^2 ?

The integral of pi(4x)^2 is (16pix^3)/3+C

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integral of pi(4x)^2

\int π (4 x)^{2} d x

\frac{16 π x ^{3}}{3} + C

Solution steps

\int π (4 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 (4 x)^{2} d x

Simplify

(4 x)^{2} : 16 x^{2}

= π \cdot \int 16 x^{2} d x

Take the constant out:

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

= π 16 \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= π 16 \cdot \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{16 π x ^{3}}{3}

Add a constant to the solution

= \frac{16 π x ^{3}}{3} + C

\int \frac{x ^{2}}{9 + x ^{2}} d x

\frac{d}{d x} ((x^{2} - 4)^{\frac{1}{3}})

x = - 2, x = 1, y = 2 x^{2} + 4, y = 0

\int x^{3} cos (n x) d x