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

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

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

\int_{0}^{3} 2 π x (x^{2}) d x

\frac{81 π}{2}

Decimal Notation

127.23450 \dots

Solution steps

\int_{0}^{3} 2 π x x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 π \cdot \int_{0}^{3} x x^{2} d x

Simplify

x x^{2} : x^{3}

= 2 π \cdot \int_{0}^{3} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{3}

= 2 π [\frac{x ^{4}}{4}]_{0}^{3}

Compute the boundaries:

\frac{81}{4}

= 2 π \frac{81}{4}

Simplify

= \frac{81 π}{2}

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