What is the integral from pi/3 to pi of 0.5-cos(x) ?

The integral from pi/3 to pi of 0.5-cos(x) is 1.91322…

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integral from pi/3 to pi of 0.5-cos(x)

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

1.91322 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{\frac{π}{3}}^{π} 0.5 d x = 1.04719 \dots

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

= 1.04719 \dots - (- \frac{3}{2})

Simplify

= 1.91322 \dots

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What is the integral from pi/3 to pi of 0.5-cos(x) ?
The integral from pi/3 to pi of 0.5-cos(x) is 1.91322…