What is the integral from 0 to 2pi of x|sin(x)| ?

The integral from 0 to 2pi of x|sin(x)| is 4pi

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integral from 0 to 2pi of x|sin(x)|

\int_{0}^{2 π} x ∣ sin (x) ∣ d x

4 π

Decimal Notation

12.56637 \dots

Solution steps

\int_{0}^{2 π} x ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} x sin (x) d x + \int_{π}^{2 π} x (- sin (x)) d x

\int_{0}^{π} x sin (x) d x = π

\int_{π}^{2 π} x (- sin (x)) d x = 3 π

= π + 3 π

Simplify

= 4 π

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What is the integral from 0 to 2pi of x|sin(x)| ?
The integral from 0 to 2pi of x|sin(x)| is 4pi