What is the integral from 0 to 70 of 0.65(70-x) ?

The integral from 0 to 70 of 0.65(70-x) is 1592.5

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integral from 0 to 70 of 0.65(70-x)

\int_{0}^{70} 0.65 (70 - x) d x

1592.5

Solution steps

\int_{0}^{70} 0.65 (70 - x) d x

Take the constant out:

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

= 0.65 \cdot \int_{0}^{70} 70 - 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

= 0.65 (\int_{0}^{70} 70 d x - \int_{0}^{70} x d x)

\int_{0}^{70} 70 d x = 4900

\int_{0}^{70} x d x = 2450

= 0.65 (4900 - 2450)

Simplify

= 1592.5

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What is the integral from 0 to 70 of 0.65(70-x) ?
The integral from 0 to 70 of 0.65(70-x) is 1592.5