What is the integral from 0 to 5pi of |sin(x)| ?

The integral from 0 to 5pi of |sin(x)| is 10

integral from 0 to 5pi of |sin(x)|

\int_{0}^{5 π} ∣ sin (x) ∣ d x

10

Solution steps

\int_{0}^{5 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_{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

= 2 + 2 + 2 + 2 + 2

Simplify

= 10

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

\int_{0}^{3} 1 + 4 r^{2} r d r

\int_{a}^{b} \frac{x ^{2}}{b - a} d x

\int_{\frac{π}{6}}^{\frac{π}{3}} 5 csc^{3} (x) d x

\int_{0}^{x} cosh^{2} (t) d t

What is the integral from 0 to 5pi of |sin(x)| ?
The integral from 0 to 5pi of |sin(x)| is 10