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

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

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

\int_{0}^{2 π} cos (\frac{x}{2}) d x

4

Solution steps

\int_{0}^{2 π} cos (\frac{x}{2}) d x

Eliminate Absolutes

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

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

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

= 2 + 2

Simplify

= 4

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