What is the integral from 20 to 30 of 0.02(30-x) ?

The integral from 20 to 30 of 0.02(30-x) is 1

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integral from 20 to 30 of 0.02(30-x)

\int_{20}^{30} 0.02 (30 - x) d x

1

Solution steps

\int_{20}^{30} 0.02 (30 - x) d x

Take the constant out:

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

= 0.02 \cdot \int_{20}^{30} 30 - 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

= 0.02 (\int_{20}^{30} 30 d x - \int_{20}^{30} x d x)

\int_{20}^{30} 30 d x = 300

\int_{20}^{30} x d x = 250

= 0.02 (300 - 250)

Simplify

= 1

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What is the integral from 20 to 30 of 0.02(30-x) ?
The integral from 20 to 30 of 0.02(30-x) is 1