What is the integral from 1 to 3.5 of 2/25 (x-1) ?

The integral from 1 to 3.5 of 2/25 (x-1) is 0.25

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integral from 1 to 3.5 of 2/25 (x-1)

\int_{1}^{3.5} \frac{2}{25} (x - 1) d x

0.25

Solution steps

\int_{1}^{3.5} \frac{2}{25} (x - 1) d x

Take the constant out:

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

= \frac{2}{25} \cdot \int_{1}^{3.5} x - 1 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{2}{25} (\int_{1}^{3.5} x d x - \int_{1}^{3.5} 1 d x)

\int_{1}^{3.5} x d x = 5.625

\int_{1}^{3.5} 1 d x = 2.5

= \frac{2}{25} (5.625 - 2.5)

Simplify

\frac{2}{25} (5.625 - 2.5) : 0.25

= 0.25

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What is the integral from 1 to 3.5 of 2/25 (x-1) ?
The integral from 1 to 3.5 of 2/25 (x-1) is 0.25