What is the integral from 0 to (3pi)/4 of |sin(2x)| ?

The integral from 0 to (3pi)/4 of |sin(2x)| is 3/2

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integral from 0 to (3pi)/4 of |sin(2x)|

\int_{0}^{\frac{3 π}{4}} ∣ sin (2 x) ∣ d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{0}^{\frac{3 π}{4}} ∣ sin (2 x) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{2}} sin (2 x) d x + \int_{\frac{π}{2}}^{\frac{3 π}{4}} - sin (2 x) d x

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

\int_{\frac{π}{2}}^{\frac{3 π}{4}} - sin (2 x) d x = \frac{1}{2}

= 1 + \frac{1}{2}

Simplify

1 + \frac{1}{2} : \frac{3}{2}

= \frac{3}{2}

What is the integral from 0 to (3pi)/4 of |sin(2x)| ?
The integral from 0 to (3pi)/4 of |sin(2x)| is 3/2