What is the integral from 0 to 2 of ((3x-6)/2) ?

The integral from 0 to 2 of ((3x-6)/2) is -3

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integral from 0 to 2 of ((3x-6)/2)

\int_{0}^{2} (\frac{3 x - 6}{2}) d x

- 3

Solution steps

\int_{0}^{2} \frac{3 x - 6}{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_{0}^{2} 3 x - 6 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_{0}^{2} 3 x d x - \int_{0}^{2} 6 d x)

\int_{0}^{2} 3 x d x = 6

\int_{0}^{2} 6 d x = 12

= \frac{1}{2} (6 - 12)

Simplify

\frac{1}{2} (6 - 12) : - 3

= - 3

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What is the integral from 0 to 2 of ((3x-6)/2) ?
The integral from 0 to 2 of ((3x-6)/2) is -3