What is the integral from 0 to 4 of sqrt(xy) ?

The integral from 0 to 4 of sqrt(xy) is (16sqrt(y))/3

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integral from 0 to 4 of sqrt(xy)

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

\frac{16 y}{3}

Solution steps

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

y x = y x

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

Take the constant out:

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

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

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

= y [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

Compute the boundaries:

\frac{16}{3}

= y \frac{16}{3}

Simplify

= \frac{16 y}{3}

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What is the integral from 0 to 4 of sqrt(xy) ?
The integral from 0 to 4 of sqrt(xy) is (16sqrt(y))/3