What is the integral from 2 to 6 of 1/8 (6-x-y) ?

The integral from 2 to 6 of 1/8 (6-x-y) is (-x+2)/2

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integral from 2 to 6 of 1/8 (6-x-y)

\int_{2}^{6} \frac{1}{8} (6 - x - y) d y

\frac{- x + 2}{2}

Solution steps

\int_{2}^{6} \frac{1}{8} (6 - x - y) d y

Take the constant out:

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

= \frac{1}{8} \cdot \int_{2}^{6} 6 - x - y d y

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}{8} (\int_{2}^{6} 6 d y - \int_{2}^{6} x d y - \int_{2}^{6} y d y)

\int_{2}^{6} 6 d y = 24

\int_{2}^{6} x d y = 4 x

\int_{2}^{6} y d y = 16

= \frac{1}{8} (24 - 4 x - 16)

Simplify

\frac{1}{8} (24 - 4 x - 16) : \frac{- x + 2}{2}

= \frac{- x + 2}{2}

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What is the integral from 2 to 6 of 1/8 (6-x-y) ?
The integral from 2 to 6 of 1/8 (6-x-y) is (-x+2)/2