What is the integral from 5 to 10 of 1/25 (10-x) ?

The integral from 5 to 10 of 1/25 (10-x) is 1/2

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integral from 5 to 10 of 1/25 (10-x)

\int_{5}^{10} \frac{1}{25} (10 - x) d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{5}^{10} \frac{1}{25} (10 - x) d x

Take the constant out:

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

= \frac{1}{25} \cdot \int_{5}^{10} 10 - 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

= \frac{1}{25} (\int_{5}^{10} 10 d x - \int_{5}^{10} x d x)

\int_{5}^{10} 10 d x = 50

\int_{5}^{10} x d x = \frac{75}{2}

= \frac{1}{25} (50 - \frac{75}{2})

Simplify

\frac{1}{25} (50 - \frac{75}{2}) : \frac{1}{2}

= \frac{1}{2}

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What is the integral from 5 to 10 of 1/25 (10-x) ?
The integral from 5 to 10 of 1/25 (10-x) is 1/2