What is the integral from 0 to y of x/y ?

The integral from 0 to y of x/y is y/2

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integral from 0 to y of x/y

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

\frac{y}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Compute the boundaries:

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

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

Simplify

= \frac{y}{2}

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What is the integral from 0 to y of x/y ?
The integral from 0 to y of x/y is y/2