What is the integral from 0 to 3pi of |sin(x)| ?

The integral from 0 to 3pi of |sin(x)| is 6

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integral from 0 to 3pi of |sin(x)|

\int_{0}^{3 π} ∣ sin (x) ∣ d x

6

Solution steps

\int_{0}^{3 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_{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

= 2 + 2 + 2

Simplify

= 6

\frac{d}{d x} (\frac{2 x}{x - 3})

f (x) = \frac{3 + x}{1 - 3 x}

\int \frac{1}{x ^{4} - 1} d x

x \to 2 lim (\frac{2 - x}{4 - x ^{2}})

\frac{d}{d x} (x^{3} + 2 x y + y^{2} + z^{2} - 5 x - 4 z)

What is the integral from 0 to 3pi of |sin(x)| ?
The integral from 0 to 3pi of |sin(x)| is 6