Solve \int_{0}^{4}\pi\left(3x\right)^{2}dx

Evaluate

\int_{0}^{4} π (3 x)^{2} d x

Multiply the terms

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\int_{0}^{4} 9 π x^{2} d x

Evaluate the integral

\int 9 π x^{2} d x

Use the property of integral \int k f (x) d x = k \int f (x) d x

9 π \times \int x^{2} d x

Use the property of integral \int x^{n} d x = \frac{x ^{n + 1}}{n + 1}

9 π \times \frac{x ^{2 + 1}}{2 + 1}

Simplify

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9 π \times \frac{x ^{3}}{3}

Cancel out the common factor 3

3 π x^{3}

Return the limits

(3 π x^{3})_{0}^{4}

Solution

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192 π

Alternative Form

\approx 603.185789