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

The integral from-pi to pi of |cos(x)| is 4

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integral from-pi to pi of |cos(x)|

\int_{- π}^{π} ∣ cos (x) ∣ d x

4

Solution steps

\int_{- π}^{π} ∣ cos (x) ∣ d x

Eliminate Absolutes

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

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

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

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

= 1 + 2 + 1

Simplify

= 4

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