What is the integral from 0 to 10pi of |sin(x)| ?

The integral from 0 to 10pi of |sin(x)| is 20

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integral from 0 to 10pi of |sin(x)|

\int_{0}^{10 π} ∣ sin (x) ∣ d x

20

Solution steps

\int_{0}^{10 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_{4 π}^{5 π} sin (x) d x + \int_{5 π}^{6 π} - sin (x) d x + \int_{6 π}^{7 π} sin (x) d x + \int_{7 π}^{8 π} - sin (x) d x + \int_{8 π}^{9 π} sin (x) d x + \int_{9 π}^{10 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

\int_{4 π}^{5 π} sin (x) d x = 2

\int_{5 π}^{6 π} - sin (x) d x = 2

\int_{6 π}^{7 π} sin (x) d x = 2

\int_{7 π}^{8 π} - sin (x) d x = 2

\int_{8 π}^{9 π} sin (x) d x = 2

\int_{9 π}^{10 π} - sin (x) d x = 2

= 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

Simplify

= 20

\int_{0}^{2} sin (\frac{nπ}{2} x) d x

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\int_{3}^{x} e^{t^{2}} d t

\int_{0}^{10} 25 - (x - 5)^{2} d x

\int_{- 1}^{1} sin (2 x) d x

What is the integral from 0 to 10pi of |sin(x)| ?
The integral from 0 to 10pi of |sin(x)| is 20