What is the integral from 0 to 1 of y/2 ?

The integral from 0 to 1 of y/2 is 1/4

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integral from 0 to 1 of y/2

\int_{0}^{1} \frac{y}{2} d y

\frac{1}{4}

Solution steps

\int_{0}^{1} \frac{y}{2} d y

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{1} y d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2}

= \frac{1}{2} \cdot \frac{1}{2}

Simplify

= \frac{1}{4}

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\int_{0}^{4} (x^{2} - 2 y^{2} + 1) d x

What is the integral from 0 to 1 of y/2 ?
The integral from 0 to 1 of y/2 is 1/4