What is the integral from 0 to 3 of 2piy(y^2) ?

The integral from 0 to 3 of 2piy(y^2) is (81pi)/2

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integral from 0 to 3 of 2piy(y^2)

\int_{0}^{3} 2 π y (y^{2}) d y

\frac{81 π}{2}

Decimal Notation

127.23450 \dots

Solution steps

\int_{0}^{3} 2 π y y^{2} d y

Take the constant out:

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

= 2 π \cdot \int_{0}^{3} y y^{2} d y

Simplify

y y^{2} : y^{3}

= 2 π \cdot \int_{0}^{3} y^{3} d y

Apply the Power Rule

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

= 2 π [\frac{y ^{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 2piy(y^2) ?
The integral from 0 to 3 of 2piy(y^2) is (81pi)/2