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Popular >

integral from-pi to pi of |t|

Solution

\int_{- π}^{π} ∣ t ∣ d t

Solution

π^{2}

+1

Decimal Notation

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}

Popular Examples

integral from 0 to y of x^2+y^2

\int_{0}^{y} x^{2} + y^{2} d x

integral from 0 to x of sqrt(4+t^6)

\int_{0}^{x} 4 + t^{6} d x

integral from 0 to 1 of sqrt(1+8t^2)

\int_{0}^{1} 1 + 8 t^{2} d t

integral from 0 to 4 of (2x-3)

\int_{0}^{4} (2 x - 3) d x

integral from 0 to 1 of pi(y-y^2)^2

\int_{0}^{1} π (y - y^{2})^{2} d y

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