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

The integral from 0 to 1/2 of 8x-1/2 x is 15/16

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

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

\frac{15}{16}

Decimal Notation

0.9375

Solution steps

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

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

\int_{0}^{\frac{1}{2}} \frac{1}{2} x d x = \frac{1}{16}

= 1 - \frac{1}{16}

Simplify

1 - \frac{1}{16} : \frac{15}{16}

= \frac{15}{16}

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What is the integral from 0 to 1/2 of 8x-1/2 x ?
The integral from 0 to 1/2 of 8x-1/2 x is 15/16