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

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

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integral from 0 to pi of-x^2

\int_{0}^{π} - x^{2} d x

- \frac{π ^{3}}{3}

Decimal

- 10.33542 \dots

Solution steps

\int_{0}^{π} - x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{0}^{π} x^{2} d x

Apply the Power Rule

= - [\frac{x ^{3}}{3}]_{0}^{π}

Compute the boundaries:

\frac{π ^{3}}{3}

= - \frac{π ^{3}}{3}

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