What is the integral from 1/4 to 1/2 of x/2 ?

The integral from 1/4 to 1/2 of x/2 is 3/64

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integral from 1/4 to 1/2 of x/2

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{x}{2} d x

\frac{3}{64}

Decimal

0.046875

Solution steps

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{x}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{\frac{1}{4}}^{\frac{1}{2}} x d x

Apply the Power Rule

= \frac{1}{2} [\frac{x ^{2}}{2}]_{\frac{1}{4}}^{\frac{1}{2}}

Compute the boundaries:

\frac{3}{32}

= \frac{1}{2} \cdot \frac{3}{32}

Simplify

= \frac{3}{64}

What is the integral from 1/4 to 1/2 of x/2 ?
The integral from 1/4 to 1/2 of x/2 is 3/64