What is the integral from 0.5 to 1.5 of (1/8+3/8 x) ?

The integral from 0.5 to 1.5 of (1/8+3/8 x) is 0.5

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integral from 0.5 to 1.5 of (1/8+3/8 x)

\int_{0.5}^{1.5} (\frac{1}{8} + \frac{3}{8} x) d x

0.5

Solution steps

\int_{0.5}^{1.5} \frac{1}{8} + \frac{3}{8} 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_{0.5}^{1.5} \frac{1}{8} d x + \int_{0.5}^{1.5} \frac{3}{8} x d x

\int_{0.5}^{1.5} \frac{1}{8} d x = 0.125

\int_{0.5}^{1.5} \frac{3}{8} x d x = 0.375

= 0.125 + 0.375

Simplify

= 0.5

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What is the integral from 0.5 to 1.5 of (1/8+3/8 x) ?
The integral from 0.5 to 1.5 of (1/8+3/8 x) is 0.5