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Popular >

integral from-pi to pi of |x|

Solution

\int_{- π}^{π} ∣ x ∣ d x

Solution

π^{2}

+1

Decimal Notation

9.86960 \dots

Solution steps

\int_{- π}^{π} ∣ x ∣ d x

Eliminate Absolutes

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

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

\int_{0}^{π} x d x = \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

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derivative of f(x)=(2x)/(1+x^2)derivative of

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\frac{\partial}{\partial x} (\frac{4 x ^{3}}{x ^{2} + y ^{2}})

(dy)/(dx)=sqrt(9y)e^{x+9}

\frac{d y}{d x} = 9 y e^{x + 9}

(\partial)/(\partial x)(1/(2sqrt(x)))

\frac{\partial}{\partial x} (\frac{1}{2 x})

Frequently Asked Questions (FAQ)

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