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

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

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integral from 5 to 10 of 2/5-1/25 x

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} x d x

\frac{1}{2}

Solution steps

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} 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

= \int_{5}^{10} \frac{2}{5} d x - \int_{5}^{10} \frac{1}{25} x d x

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

\int_{5}^{10} \frac{1}{25} x d x = \frac{3}{2}

= 2 - \frac{3}{2}

Simplify

2 - \frac{3}{2} : \frac{1}{2}

= \frac{1}{2}

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