What is the integral from 0 to 1 of xy^2 ?

The integral from 0 to 1 of xy^2 is (y^2)/2

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integral from 0 to 1 of xy^2

\int_{0}^{1} x y^{2} d x

\frac{y ^{2}}{2}

Solution steps

\int_{0}^{1} x y^{2} d x

Take the constant out:

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

= y^{2} \cdot \int_{0}^{1} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{1}

= y^{2} [\frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= y^{2} \frac{1}{2}

Simplify

= \frac{y ^{2}}{2}

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What is the integral from 0 to 1 of xy^2 ?
The integral from 0 to 1 of xy^2 is (y^2)/2