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

The integral from 0 to 4 of pi(2x)^2 is (256pi)/3

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

\int_{0}^{4} π (2 x)^{2} d x

\frac{256 π}{3}

Decimal

268.08257 \dots

Solution steps

\int_{0}^{4} 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}^{4} (2 x)^{2} d x

Simplify

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

= π \cdot \int_{0}^{4} 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}^{4} x^{2} d x

Apply the Power Rule

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

= π 4 [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= π 4 \cdot \frac{64}{3}

Simplify

= \frac{256 π}{3}

\frac{d}{d x} (x ln (x) - x + 1)

\int \frac{( 1 + 15 x )}{x} d x

\int \frac{x + 5}{x + 1} d x

x \to - 2 lim (x - 5)

\int \frac{x}{x ^{2} - 4 x} d x

What is the integral from 0 to 4 of pi(2x)^2 ?
The integral from 0 to 4 of pi(2x)^2 is (256pi)/3