What is the integral from 0 to 1 of (-1+(pix)/2) ?

The integral from 0 to 1 of (-1+(pix)/2) is -1+pi/4

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integral from 0 to 1 of (-1+(pix)/2)

\int_{0}^{1} (- 1 + \frac{π x}{2}) d x

- 1 + \frac{π}{4}

Decimal

- 0.21460 \dots

Solution steps

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

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

\int_{0}^{1} \frac{π x}{2} d x = \frac{π}{4}

= - 1 + \frac{π}{4}

What is the integral from 0 to 1 of (-1+(pix)/2) ?
The integral from 0 to 1 of (-1+(pix)/2) is -1+pi/4