What is the integral from 4 to 5 of 1/2 (5-x) ?

The integral from 4 to 5 of 1/2 (5-x) is 1/4

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integral from 4 to 5 of 1/2 (5-x)

\int_{4}^{5} \frac{1}{2} (5 - x) d x

\frac{1}{4}

Decimal Notation

0.25

Solution steps

\int_{4}^{5} \frac{1}{2} (5 - x) 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_{4}^{5} 5 - 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_{4}^{5} 5 d x - \int_{4}^{5} x d x)

\int_{4}^{5} 5 d x = 5

\int_{4}^{5} x d x = \frac{9}{2}

= \frac{1}{2} (5 - \frac{9}{2})

Simplify

\frac{1}{2} (5 - \frac{9}{2}) : \frac{1}{4}

= \frac{1}{4}

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What is the integral from 4 to 5 of 1/2 (5-x) ?
The integral from 4 to 5 of 1/2 (5-x) is 1/4