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

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

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integral from 0 to pi of |cos(2x)|

\int_{0}^{π} ∣ cos (2 x) ∣ d x

2

Solution steps

\int_{0}^{π} ∣ cos (2 x) ∣ d x

Eliminate Absolutes

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

\int_{0}^{\frac{π}{4}} cos (2 x) d x = \frac{1}{2}

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

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

= \frac{1}{2} + 1 + \frac{1}{2}

Simplify

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

= 2

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