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

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

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integral from 0 to pi of |sin(x)|

\int_{0}^{π} ∣ sin (x) ∣ d x

2

Solution steps

\int_{0}^{π} ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= [- cos (x)]_{0}^{π}

Compute the boundaries:

2

= 2

\int_{1}^{e} \frac{2 x ^{2} + 1}{2 x} d x

\int_{0}^{2 π} cos (2 θ) d θ

\int_{0}^{\frac{π}{3}} sec (θ) tan (θ) d θ

\int_{0}^{2 π} 1 + x^{2} d x

\int_{1}^{3 x} x^{3} e^{x y} d y

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