What is the integral from 1 to 2 of (x-1)/2 ?

The integral from 1 to 2 of (x-1)/2 is 1/4

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integral from 1 to 2 of (x-1)/2

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

\frac{1}{4}

Decimal

0.25

Solution steps

\int_{1}^{2} \frac{x - 1}{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_{1}^{2} x - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{1}^{2} x d x - \int_{1}^{2} 1 d x)

\int_{1}^{2} x d x = \frac{3}{2}

\int_{1}^{2} 1 d x = 1

= \frac{1}{2} (\frac{3}{2} - 1)

Simplify

\frac{1}{2} (\frac{3}{2} - 1) : \frac{1}{4}

= \frac{1}{4}

What is the integral from 1 to 2 of (x-1)/2 ?
The integral from 1 to 2 of (x-1)/2 is 1/4