What is the integral from pi/3 to pi of |cos(x)| ?

The integral from pi/3 to pi of |cos(x)| is -(sqrt(3))/2+2

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integral from pi/3 to pi of |cos(x)|

\int_{\frac{π}{3}}^{π} ∣ cos (x) ∣ d x

- \frac{3}{2} + 2

Solution steps

\int_{\frac{π}{3}}^{π} ∣ cos (x) ∣ d x

Eliminate Absolutes

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

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

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

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

Simplify

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

\int_{0}^{1} 3 x^{2} - 1 d x

\int_{0}^{0.3} ln (1 + x^{2}) d x

\int_{- 2 π}^{2 π} x \cdot sin (0.5 x) d x

\int_{1}^{3} \frac{2 x}{( x ^{2} + 2 ) ^{2}} d x

\int_{1}^{2} (2 x^{3} - 2 x^{2} - 4 x - 1) d x

What is the integral from pi/3 to pi of |cos(x)| ?
The integral from pi/3 to pi of |cos(x)| is -(sqrt(3))/2+2