What is the integral from 0 to 2pi of 1-|cos(x)| ?

The integral from 0 to 2pi of 1-|cos(x)| is 2pi-4

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integral from 0 to 2pi of 1-|cos(x)|

\int_{0}^{2 π} 1 - ∣ cos (x) ∣ d x

2 π - 4

Decimal

2.28318 \dots

Solution steps

\int_{0}^{2 π} 1 - ∣ cos (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{2}} 1 - cos (x) d x + \int_{\frac{π}{2}}^{\frac{3 π}{2}} 1 - (- cos (x)) d x + \int_{\frac{3 π}{2}}^{2 π} 1 - cos (x) d x

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

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

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

= \frac{π}{2} - 1 + π - 2 + 2 π - \frac{3 π}{2} - 1

Simplify

\frac{π}{2} - 1 + π - 2 + 2 π - \frac{3 π}{2} - 1 : 2 π - 4

= 2 π - 4

\int_{0}^{1} \frac{x ^{2} + x + 1}{x + 1} d x

\int_{- 2}^{x} f (t) d t

\int_{4}^{6} x^{2} + x - 9 d x

\int_{- 1}^{1} x^{2} + 3 d x

\int_{0}^{b} \frac{x}{x ^{2} + 1} d x

What is the integral from 0 to 2pi of 1-|cos(x)| ?
The integral from 0 to 2pi of 1-|cos(x)| is 2pi-4