What is the integral from 1 to 1.5 of 2/5 (x+1) ?

The integral from 1 to 1.5 of 2/5 (x+1) is 0.45

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integral from 1 to 1.5 of 2/5 (x+1)

\int_{1}^{1.5} \frac{2}{5} (x + 1) d x

0.45

Solution steps

\int_{1}^{1.5} \frac{2}{5} (x + 1) d x

Take the constant out:

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

= \frac{2}{5} \cdot \int_{1}^{1.5} 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}{5} (\int_{1}^{1.5} x d x + \int_{1}^{1.5} 1 d x)

\int_{1}^{1.5} x d x = 0.625

\int_{1}^{1.5} 1 d x = 0.5

= \frac{2}{5} (0.625 + 0.5)

Simplify

\frac{2}{5} (0.625 + 0.5) : 0.45

= 0.45

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What is the integral from 1 to 1.5 of 2/5 (x+1) ?
The integral from 1 to 1.5 of 2/5 (x+1) is 0.45