What is the integral from 0 to 0.5 of 96x^2y^3 ?

The integral from 0 to 0.5 of 96x^2y^3 is 4.00000…y^3

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integral from 0 to 0.5 of 96x^2y^3

\int_{0}^{0.5} 96 x^{2} y^{3} d x

4.00000 \dots y^{3}

Solution steps

\int_{0}^{0.5} 96 x^{2} y^{3} d x

Take the constant out:

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

= 96 y^{3} \cdot \int_{0}^{0.5} x^{2} d x

Apply the Power Rule

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

= 96 y^{3} [\frac{x ^{3}}{3}]_{0}^{0.5}

Simplify

= 96 y^{3} [0.33333 \dots x^{3}]_{0}^{0.5}

Compute the boundaries:

0.04166 \dots

= 96 y^{3} \cdot 0.04166 \dots

Simplify

= 4.00000 \dots y^{3}

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What is the integral from 0 to 0.5 of 96x^2y^3 ?
The integral from 0 to 0.5 of 96x^2y^3 is 4.00000…y^3