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Popular Calculus >

integral from-pi to pi of |t|

Solution

\int_{- π}^{π} ∣ t ∣ d t

Solution

π^{2}

+1

Decimal

9.86960 \dots

Solution steps

\int_{- π}^{π} ∣ t ∣ d t

Eliminate Absolutes

= \int_{- π}^{0} - t d t + \int_{0}^{π} t d t

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

\int_{0}^{π} t d t = \frac{π ^{2}}{2}

= \frac{π ^{2}}{2} + \frac{π ^{2}}{2}

Simplify

\frac{π ^{2}}{2} + \frac{π ^{2}}{2} : π^{2}

= π^{2}

Graph

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Frequently Asked Questions (FAQ)

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