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

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

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

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

2

Solution steps

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

Eliminate Absolutes

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

\int_{- \frac{π}{2}}^{0} - sin (x) d x = 1

\int_{0}^{\frac{π}{2}} sin (x) d x = 1

= 1 + 1

Simplify

= 2

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