What is the integral from 2 to 8 of |sin(x)| ?

The integral from 2 to 8 of |sin(x)| is 4+cos(2)-cos(8)

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integral from 2 to 8 of |sin(x)|

\int_{2}^{8} ∣ sin (x) ∣ d x

4 + cos (2) - cos (8)

Solution steps

\int_{2}^{8} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{2}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{8} sin (x) d x

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

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{8} sin (x) d x = - cos (8) + 1

= 1 + cos (2) + 2 - cos (8) + 1

Simplify

= 4 + cos (2) - cos (8)

\int_{2}^{4} 4^{2 x} d x

\int_{0}^{z} \frac{z}{x ^{2} + z ^{2}} d x

\int_{2}^{3} 4^{5 x} d x

\int_{- 2}^{2} (3 + 4 - x^{2}) d x

\int_{0}^{π} sin (2 x) cos (2 x) d x

What is the integral from 2 to 8 of |sin(x)| ?
The integral from 2 to 8 of |sin(x)| is 4+cos(2)-cos(8)