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

\int_{1}^{3} \frac{5 x}{1 + x ^{2}} d x

\int_{1}^{x^{3}} \frac{1}{1 + ln ( t )} d t

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

\int_{2}^{0} x d x

\int_{1}^{2} 2 x (x^{2} + 1) d x

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