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

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

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

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

3

Solution steps

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

Eliminate Absolutes

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

\int_{0}^{π} sin (x) d x = 2

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

= 2 + 1

Simplify

= 3

\int_{1}^{4} \frac{1}{x ( 2 + x )} d x

\int_{3}^{4} \frac{e ^{l n (x)}}{x} d x

\int_{- 1}^{4} \frac{2 x ^{3}}{x ^{2} - 4} d x

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

\int_{1}^{3} x^{2} + x^{4} d x

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