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

The integral from 5 to x of 2/5-1/25 x is (2x)/5-2-(x^2-25)/(50)

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

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

\frac{2 x}{5} - 2 - \frac{x ^{2} - 25}{50}

Solution steps

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

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

\int_{5}^{x} \frac{1}{25} x d x = \frac{x ^{2} - 25}{50}

= \frac{2 x}{5} - 2 - \frac{x ^{2} - 25}{50}

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What is the integral from 5 to x of 2/5-1/25 x ?
The integral from 5 to x of 2/5-1/25 x is (2x)/5-2-(x^2-25)/(50)