What is the integral from y to 2y of xy ?

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

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integral from y to 2y of xy

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

y (2 y^{2} - \frac{y ^{2}}{2})

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{y}^{2 y}

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

Compute the boundaries:

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

= y (2 y^{2} - \frac{y ^{2}}{2})

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