What is the integral from 0 to pi of (pi-x) ?

The integral from 0 to pi of (pi-x) is pi^2-(pi^2)/2

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integral from 0 to pi of (pi-x)

\int_{0}^{π} (π - x) d x

π^{2} - \frac{π ^{2}}{2}

Decimal

4.93480 \dots

Solution steps

\int_{0}^{π} π - 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}^{π} π d x - \int_{0}^{π} x d x

\int_{0}^{π} π d x = π^{2}

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

= π^{2} - \frac{π ^{2}}{2}

What is the integral from 0 to pi of (pi-x) ?
The integral from 0 to pi of (pi-x) is pi^2-(pi^2)/2