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

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

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integral from 0 to x of y/x

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

\frac{x}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Compute the boundaries:

\frac{x ^{2}}{2}

= \frac{\frac{x ^{2}}{2}}{x}

Simplify

= \frac{x}{2}

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