What is the integral from 0 to 4 of pi(3x)^2 ?

The integral from 0 to 4 of pi(3x)^2 is 192pi

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integral from 0 to 4 of pi(3x)^2

\int_{0}^{4} π (3 x)^{2} d x

192 π

Decimal Notation

603.18578 \dots

Solution steps

\int_{0}^{4} π (3 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}^{4} (3 x)^{2} d x

Simplify

(3 x)^{2} : 9 x^{2}

= π \cdot \int_{0}^{4} 9 x^{2} d x

Take the constant out:

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

= π 9 \cdot \int_{0}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{4}

= π 9 [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= π 9 \cdot \frac{64}{3}

Simplify

= 192 π

f (x) = cos (tan (x))

y^{^{''}} + a y^{^{'}} + b y = t + e^{3 t}

x \to - 1 lim (ln (x + 1))

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 4 y^{2}))

\frac{\partial}{\partial x} (\frac{1}{2 x})

What is the integral from 0 to 4 of pi(3x)^2 ?
The integral from 0 to 4 of pi(3x)^2 is 192pi