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

The integral from pi to (3pi)/2 of |sin(x)| is 1

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

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

1

Solution steps

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

Eliminate Absolutes

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= - [- cos (x)]_{π}^{\frac{3 π}{2}}

Compute the boundaries:

- 1

= - (- 1)

Simplify

= 1

\int_{5}^{x} \frac{1}{t} d t

\int_{0}^{π} 2 x sin (2 x) d x

\int_{0}^{5} 1 - - x^{2} + 5 x - 4 d x

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

\int_{2}^{e} \frac{x ^{4} - 5 x}{x ^{2}} d x

What is the integral from pi to (3pi)/2 of |sin(x)| ?
The integral from pi to (3pi)/2 of |sin(x)| is 1