What is the integral from 0 to pi/3 of cos(x)-1/2 ?

The integral from 0 to pi/3 of cos(x)-1/2 is (sqrt(3))/2-pi/6

integral from 0 to pi/3 of cos(x)-1/2

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

\frac{3}{2} - \frac{π}{6}

Decimal

0.34242 \dots

Solution steps

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

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

\int_{0}^{\frac{π}{3}} \frac{1}{2} d x = \frac{π}{6}

= \frac{3}{2} - \frac{π}{6}

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What is the integral from 0 to pi/3 of cos(x)-1/2 ?
The integral from 0 to pi/3 of cos(x)-1/2 is (sqrt(3))/2-pi/6