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

The integral from 0 to 6 of (6-x)(6) is 108

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integral from 0 to 6 of (6-x)(6)

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

108

Solution steps

\int_{0}^{6} (6 - x) \cdot 6 d x

Take the constant out:

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

= 6 \cdot \int_{0}^{6} 6 - 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

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

\int_{0}^{6} 6 d x = 36

\int_{0}^{6} x d x = 18

= 6 (36 - 18)

Simplify

= 108

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What is the integral from 0 to 6 of (6-x)(6) ?
The integral from 0 to 6 of (6-x)(6) is 108