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Popular >

integral of (2-x)/2

Solution

\int \frac{2 - x}{2} d x

Solution

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

Solution steps

\int \frac{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 2 - x 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 2 d x - \int x d x)

\int 2 d x = 2 x

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

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

Simplify

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

What is the integral of (2-x)/2 ?
The integral of (2-x)/2 is x-(x^2)/4+C