What is the integral from 3 to 9 of |sin(x)| ?

The integral from 3 to 9 of |sin(x)| is 4+cos(3)-cos(9)

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integral from 3 to 9 of |sin(x)|

\int_{3}^{9} ∣ sin (x) ∣ d x

4 + cos (3) - cos (9)

Decimal Notation

3.92113 \dots

Solution steps

\int_{3}^{9} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{3}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{9} sin (x) d x

\int_{3}^{π} sin (x) d x = 1 + cos (3)

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{9} sin (x) d x = - cos (9) + 1

= 1 + cos (3) + 2 - cos (9) + 1

Simplify

= 4 + cos (3) - cos (9)

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

\int_{2}^{5} 3 x^{2} d x

\int_{π}^{2 π} (x - 2 sin (x)) d x

What is the integral from 3 to 9 of |sin(x)| ?
The integral from 3 to 9 of |sin(x)| is 4+cos(3)-cos(9)