What is the integral from 0 to 0.5 of 8y^2 ?

The integral from 0 to 0.5 of 8y^2 is 0.33333…

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integral from 0 to 0.5 of 8y^2

\int_{0}^{0.5} 8 y^{2} d y

0.33333 \dots

Solution steps

\int_{0}^{0.5} 8 y^{2} d y

Take the constant out:

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

= 8 \cdot \int_{0}^{0.5} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{0}^{0.5}

= 8 [\frac{y ^{3}}{3}]_{0}^{0.5}

Simplify

= 8 [0.33333 \dots y^{3}]_{0}^{0.5}

Compute the boundaries:

0.04166 \dots

= 8 \cdot 0.04166 \dots

Simplify

= 0.33333 \dots

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What is the integral from 0 to 0.5 of 8y^2 ?
The integral from 0 to 0.5 of 8y^2 is 0.33333…