What is the integral from 0 to 2 of 0.125(6-x-y) ?

The integral from 0 to 2 of 0.125(6-x-y) is 0.125(-2y+10)

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integral from 0 to 2 of 0.125(6-x-y)

\int_{0}^{2} 0.125 (6 - x - y) d x

0.125 (- 2 y + 10)

Solution steps

\int_{0}^{2} 0.125 (6 - x - y) d x

Take the constant out:

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

= 0.125 \cdot \int_{0}^{2} 6 - y - 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

= 0.125 (\int_{0}^{2} 6 d x - \int_{0}^{2} y d x - \int_{0}^{2} x d x)

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

\int_{0}^{2} y d x = 2 y

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

= 0.125 (12 - 2 y - 2)

Simplify

= 0.125 (- 2 y + 10)

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What is the integral from 0 to 2 of 0.125(6-x-y) ?
The integral from 0 to 2 of 0.125(6-x-y) is 0.125(-2y+10)