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

The integral from 0 to 4pi of |sin(x)| is 8

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

\int_{0}^{4 π} ∣ sin (x) ∣ d x

8

Solution steps

\int_{0}^{4 π} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{3 π} sin (x) d x + \int_{3 π}^{4 π} - sin (x) d x

\int_{0}^{π} sin (x) d x = 2

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{3 π} sin (x) d x = 2

\int_{3 π}^{4 π} - sin (x) d x = 2

= 2 + 2 + 2 + 2

Simplify

= 8

What is the integral from 0 to 4pi of |sin(x)| ?
The integral from 0 to 4pi of |sin(x)| is 8