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

The integral of 1/2 (x-2) is (x^2)/4-x+C

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integral of 1/2 (x-2)

\int \frac{1}{2} (x - 2) d x

\frac{x ^{2}}{4} - x + C

Solution steps

\int \frac{1}{2} (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 x - 2 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 x d x - \int 2 d x)

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

\int 2 d x = 2 x

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

Simplify

\frac{1}{2} (\frac{x ^{2}}{2} - 2 x) : \frac{x ^{2}}{4} - x

= \frac{x ^{2}}{4} - x

Add a constant to the solution

= \frac{x ^{2}}{4} - x + C

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