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

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

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integral from-pi to pi of t^2

\int_{- π}^{π} t^{2} d t

\frac{2 π ^{3}}{3}

Decimal

20.67085 \dots

Solution steps

\int_{- π}^{π} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{- π}^{π}

= [\frac{t ^{3}}{3}]_{- π}^{π}

Compute the boundaries:

2 \cdot \frac{π ^{3}}{3}

= 2 \cdot \frac{π ^{3}}{3}

Simplify

= \frac{2 π ^{3}}{3}

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