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

The integral from 0 to 3 of pi(3x^2)^2 is (2187pi)/5

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

\int_{0}^{3} π (3 x^{2})^{2} d x

\frac{2187 π}{5}

Decimal

1374.13262 \dots

Solution steps

\int_{0}^{3} π (3 x^{2})^{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})^{2} d x

Simplify

(3 x^{2})^{2} : 9 x^{4}

= π \cdot \int_{0}^{3} 9 x^{4} 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^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{3}

= π 9 [\frac{x ^{5}}{5}]_{0}^{3}

Compute the boundaries:

\frac{243}{5}

= π 9 \cdot \frac{243}{5}

Simplify

= \frac{2187 π}{5}

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What is the integral from 0 to 3 of pi(3x^2)^2 ?
The integral from 0 to 3 of pi(3x^2)^2 is (2187pi)/5