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

The integral from 0 to 4 of pi(4x)^2 is (1024pi)/3

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

\int_{0}^{4} π (4 x)^{2} d x

\frac{1024 π}{3}

Decimal Notation

1072.33029 \dots

Solution steps

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

Simplify

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

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

Apply the Power Rule

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

= π 16 [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= π 16 \cdot \frac{64}{3}

Simplify

= \frac{1024 π}{3}

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What is the integral from 0 to 4 of pi(4x)^2 ?
The integral from 0 to 4 of pi(4x)^2 is (1024pi)/3