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

The integral from 0 to pi of (pi^2-x^2) is pi^3-(pi^3)/3

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

\int_{0}^{π} (π^{2} - x^{2}) d x

π^{3} - \frac{π ^{3}}{3}

Decimal Notation

20.67085 \dots

Solution steps

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

\int_{0}^{π} π^{2} d x = π^{3}

\int_{0}^{π} x^{2} d x = \frac{π ^{3}}{3}

= π^{3} - \frac{π ^{3}}{3}

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What is the integral from 0 to pi of (pi^2-x^2) ?
The integral from 0 to pi of (pi^2-x^2) is pi^3-(pi^3)/3