What is the integral from 0 to 0.5 of 8x-1/2 x ?

The integral from 0 to 0.5 of 8x-1/2 x is 0.9375

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integral from 0 to 0.5 of 8x-1/2 x

\int_{0}^{0.5} 8 x - \frac{1}{2} x d x

0.9375

Solution steps

\int_{0}^{0.5} 8 x - \frac{1}{2} 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}^{0.5} 8 x d x - \int_{0}^{0.5} \frac{1}{2} x d x

\int_{0}^{0.5} 8 x d x = 1

\int_{0}^{0.5} \frac{1}{2} x d x = 0.0625

= 1 - 0.0625

Simplify

= 0.9375

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What is the integral from 0 to 0.5 of 8x-1/2 x ?
The integral from 0 to 0.5 of 8x-1/2 x is 0.9375