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

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

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integral from pi/4 to pi of |cos(x)|

\int_{\frac{π}{4}}^{π} ∣ cos (x) ∣ d x

- \frac{1}{2} + 2

Solution steps

\int_{\frac{π}{4}}^{π} ∣ cos (x) ∣ d x

Eliminate Absolutes

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

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

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

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

Simplify

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

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