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

The integral from 2 to 6 of (2x-3)/2 is 10

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

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

10

Solution steps

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

\int_{2}^{6} 2 x d x = 32

\int_{2}^{6} 3 d x = 12

= \frac{1}{2} (32 - 12)

Simplify

\frac{1}{2} (32 - 12) : 10

= 10

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What is the integral from 2 to 6 of (2x-3)/2 ?
The integral from 2 to 6 of (2x-3)/2 is 10