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

The integral from-1 to 1 of xy^2 is (2x)/3

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integral from-1 to 1 of xy^2

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

\frac{2 x}{3}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{- 1}^{1}

= x [\frac{y ^{3}}{3}]_{- 1}^{1}

Compute the boundaries:

\frac{2}{3}

= x \frac{2}{3}

Simplify

= \frac{2 x}{3}

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What is the integral from-1 to 1 of xy^2 ?
The integral from-1 to 1 of xy^2 is (2x)/3