What is the integral from 0 to 6 of pi(2x)^2 ?

The integral from 0 to 6 of pi(2x)^2 is 288pi

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integral from 0 to 6 of pi(2x)^2

\int_{0}^{6} π (2 x)^{2} d x

288 π

Decimal Notation

904.77868 \dots

Solution steps

\int_{0}^{6} 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_{0}^{6} (2 x)^{2} d x

Simplify

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

= π \cdot \int_{0}^{6} 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_{0}^{6} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{6}

= π 4 [\frac{x ^{3}}{3}]_{0}^{6}

Compute the boundaries:

72

= π 4 \cdot 72

Simplify

= 288 π

\frac{d}{d x} (ln (\frac{x ^{2}}{x + 1}))

\int \frac{( cos ( x ) )}{( ( sin ^{2} ( x ) ) ^{\frac{1}{3}} )} d x

\frac{d}{d t} (t^{2} + 4 t)

y^{^{'}} + 10 y = 1

x \to 0 lim (2 + (\frac{3}{x}))

What is the integral from 0 to 6 of pi(2x)^2 ?
The integral from 0 to 6 of pi(2x)^2 is 288pi