What is the integral from 0 to (3pi)/2 of 8|sin(x)| ?

The integral from 0 to (3pi)/2 of 8|sin(x)| is 24

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integral from 0 to (3pi)/2 of 8|sin(x)|

\int_{0}^{\frac{3 π}{2}} 8 ∣ sin (x) ∣ d x

24

Solution steps

\int_{0}^{\frac{3 π}{2}} 8 ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} 8 sin (x) d x + \int_{π}^{\frac{3 π}{2}} 8 (- sin (x)) d x

\int_{0}^{π} 8 sin (x) d x = 16

\int_{π}^{\frac{3 π}{2}} 8 (- sin (x)) d x = 8

= 16 + 8

Simplify

= 24

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What is the integral from 0 to (3pi)/2 of 8|sin(x)| ?
The integral from 0 to (3pi)/2 of 8|sin(x)| is 24