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

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

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integral from-pi to 0 of pi-x

\int_{- π}^{0} π - x d x

π^{2} + \frac{π ^{2}}{2}

Solution steps

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

\int_{- π}^{0} π d x = π^{2}

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

= π^{2} - (- \frac{π ^{2}}{2})

Simplify

= π^{2} + \frac{π ^{2}}{2}

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