What is the integral from 2pi to 5pi of |sin(x)| ?

The integral from 2pi to 5pi of |sin(x)| is 6

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integral from 2pi to 5pi of |sin(x)|

\int_{2 π}^{5 π} ∣ sin (x) ∣ d x

6

Solution steps

\int_{2 π}^{5 π} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{2 π}^{3 π} sin (x) d x + \int_{3 π}^{4 π} - sin (x) d x + \int_{4 π}^{5 π} sin (x) d x

\int_{2 π}^{3 π} sin (x) d x = 2

\int_{3 π}^{4 π} - sin (x) d x = 2

\int_{4 π}^{5 π} sin (x) d x = 2

= 2 + 2 + 2

Simplify

= 6

\int_{1}^{3} \frac{2}{t} d t

\int_{- 1}^{2} x^{2} d x

\int_{0}^{π} 4 sin (x) - sin (4 x) d x

\int_{0}^{\infty} \frac{3}{x} d x

\int_{0}^{3} (x^{2} - 2 x - 3) d x

What is the integral from 2pi to 5pi of |sin(x)| ?
The integral from 2pi to 5pi of |sin(x)| is 6