What is the integral from 0 to (3pi)/2 of 4|sin(x)| ?

The integral from 0 to (3pi)/2 of 4|sin(x)| is 12

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integral from 0 to (3pi)/2 of 4|sin(x)|

\int_{0}^{\frac{3 π}{2}} 4 ∣ sin (x) ∣ d x

12

Solution steps

\int_{0}^{\frac{3 π}{2}} 4 ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} 4 sin (x) d x + \int_{π}^{\frac{3 π}{2}} 4 (- sin (x)) d x

\int_{0}^{π} 4 sin (x) d x = 8

\int_{π}^{\frac{3 π}{2}} 4 (- sin (x)) d x = 4

= 8 + 4

Simplify

= 12

What is the integral from 0 to (3pi)/2 of 4|sin(x)| ?
The integral from 0 to (3pi)/2 of 4|sin(x)| is 12