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

The integral from 0 to 3 of 2y^2 is 18

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integral from 0 to 3 of 2y^2

\int_{0}^{3} 2 y^{2} d y

18

Solution steps

\int_{0}^{3} 2 y^{2} d y

Take the constant out:

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

= 2 \cdot \int_{0}^{3} y^{2} d y

Apply the Power Rule

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

= 2 [\frac{y ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= 2 \cdot 9

Simplify

= 18

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What is the integral from 0 to 3 of 2y^2 ?
The integral from 0 to 3 of 2y^2 is 18