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

The integral from 0 to 3 of pi(3x)^2 is 81pi

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

\int_{0}^{3} π (3 x)^{2} d x

81 π

Decimal

254.46900 \dots

Solution steps

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

Simplify

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

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

Apply the Power Rule

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

= π 9 [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= π 9 \cdot 9

Simplify

= 81 π

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What is the integral from 0 to 3 of pi(3x)^2 ?
The integral from 0 to 3 of pi(3x)^2 is 81pi