What is the integral from 0 to 4 of 2xy ?

The integral from 0 to 4 of 2xy is 16x

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integral from 0 to 4 of 2xy

\int_{0}^{4} 2 x y d y

16 x

Solution steps

\int_{0}^{4} 2 x y d y

Take the constant out:

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

= 2 x \cdot \int_{0}^{4} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{4}

= 2 x [\frac{y ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= 2 x \cdot 8

Simplify

= 16 x

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What is the integral from 0 to 4 of 2xy ?
The integral from 0 to 4 of 2xy is 16x