What is the integral from 0 to y of xyz ?

The integral from 0 to y of xyz is (y^3z)/2

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integral from 0 to y of xyz

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

\frac{y ^{3} z}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

= yz \frac{y ^{2}}{2}

Simplify

= \frac{y ^{3} z}{2}

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What is the integral from 0 to y of xyz ?
The integral from 0 to y of xyz is (y^3z)/2