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

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

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

\int_{0}^{2 π} ∣ sin (x) ∣ d x

4

Solution steps

\int_{0}^{2 π} ∣ sin (x) ∣ d x

Eliminate Absolutes

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

\int_{0}^{π} sin (x) d x = 2

\int_{π}^{2 π} - sin (x) d x = 2

= 2 + 2

Simplify

= 4

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