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

The integral from 0 to 3 of pi(2x^2)^2 is (972pi)/5

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

\int_{0}^{3} π (2 x^{2})^{2} d x

\frac{972 π}{5}

Decimal Notation

610.72561 \dots

Solution steps

\int_{0}^{3} π (2 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} (2 x^{2})^{2} d x

Simplify

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

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

Apply the Power Rule

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

= π 4 [\frac{x ^{5}}{5}]_{0}^{3}

Compute the boundaries:

\frac{243}{5}

= π 4 \cdot \frac{243}{5}

Simplify

= \frac{972 π}{5}

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What is the integral from 0 to 3 of pi(2x^2)^2 ?
The integral from 0 to 3 of pi(2x^2)^2 is (972pi)/5