What is the integral from 0 to pi of |cos(x)-0.5| ?

The integral from 0 to pi of |cos(x)-0.5| is 2.25564…

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integral from 0 to pi of |cos(x)-0.5|

\int_{0}^{π} ∣ cos (x) - 0.5 ∣ d x

2.25564 \dots

Solution steps

\int_{0}^{π} ∣ cos (x) - 0.5 ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{3}} cos (x) - 0.5 d x + \int_{\frac{π}{3}}^{π} - cos (x) + 0.5 d x

\int_{0}^{\frac{π}{3}} cos (x) - 0.5 d x = 0.34242 \dots

\int_{\frac{π}{3}}^{π} - cos (x) + 0.5 d x = 1.91322 \dots

= 0.34242 \dots + 1.91322 \dots

Simplify

= 2.25564 \dots

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What is the integral from 0 to pi of |cos(x)-0.5| ?
The integral from 0 to pi of |cos(x)-0.5| is 2.25564…