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

The integral from 0 to 1 of 2xy is y

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integral from 0 to 1 of 2xy

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

y

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

Compute the boundaries:

\frac{1}{2}

= 2 y \frac{1}{2}

Simplify

= y