What is the integral from 3 to 6 of (2x-3)/6 ?

The integral from 3 to 6 of (2x-3)/6 is 3

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integral from 3 to 6 of (2x-3)/6

\int_{3}^{6} \frac{2 x - 3}{6} d x

3

Solution steps

\int_{3}^{6} \frac{2 x - 3}{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_{3}^{6} 2 x - 3 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_{3}^{6} 2 x d x - \int_{3}^{6} 3 d x)

\int_{3}^{6} 2 x d x = 27

\int_{3}^{6} 3 d x = 9

= \frac{1}{6} (27 - 9)

Simplify

\frac{1}{6} (27 - 9) : 3

= 3

What is the integral from 3 to 6 of (2x-3)/6 ?
The integral from 3 to 6 of (2x-3)/6 is 3