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

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

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

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

3

Solution steps

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

Eliminate Absolutes

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

\int_{0}^{π} sin (x) d x = 2

\int_{π}^{\frac{3 π}{2}} - sin (x) d x = 1

= 2 + 1

Simplify

= 3

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