What is the integral from 0 to 0.5 of 2(1-x) ?

The integral from 0 to 0.5 of 2(1-x) is 0.75

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integral from 0 to 0.5 of 2(1-x)

\int_{0}^{0.5} 2 (1 - x) d x

0.75

Solution steps

\int_{0}^{0.5} 2 (1 - x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{0.5} 1 - 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

= 2 (\int_{0}^{0.5} 1 d x - \int_{0}^{0.5} x d x)

\int_{0}^{0.5} 1 d x = 0.5

\int_{0}^{0.5} x d x = 0.125

= 2 (0.5 - 0.125)

Simplify

= 0.75

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What is the integral from 0 to 0.5 of 2(1-x) ?
The integral from 0 to 0.5 of 2(1-x) is 0.75