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

The integral from 0 to 3 of pi(4x)^2 is 144pi

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

\int_{0}^{3} π (4 x)^{2} d x

144 π

Decimal

452.38934 \dots

Solution steps

\int_{0}^{3} 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}^{3} (4 x)^{2} d x

Simplify

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

= π \cdot \int_{0}^{3} 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}^{3} x^{2} d x

Apply the Power Rule

= π 16 [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= π 16 \cdot 9

Simplify

= 144 π

What is the integral from 0 to 3 of pi(4x)^2 ?
The integral from 0 to 3 of pi(4x)^2 is 144pi