What is the integral from 4 to 4.5 of (6-x)/6 ?

The integral from 4 to 4.5 of (6-x)/6 is 0.14583…

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integral from 4 to 4.5 of (6-x)/6

\int_{4}^{4.5} \frac{6 - x}{6} d x

0.14583 \dots

Solution steps

\int_{4}^{4.5} \frac{6 - x}{6} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int_{4}^{4.5} 6 - 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}{6} (\int_{4}^{4.5} 6 d x - \int_{4}^{4.5} x d x)

\int_{4}^{4.5} 6 d x = 3

\int_{4}^{4.5} x d x = 2.125

= \frac{1}{6} (3 - 2.125)

Simplify

\frac{1}{6} (3 - 2.125) : 0.14583 \dots

= 0.14583 \dots

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What is the integral from 4 to 4.5 of (6-x)/6 ?
The integral from 4 to 4.5 of (6-x)/6 is 0.14583…