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

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

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

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

3 - \frac{π}{3}

Decimal Notation

0.68485 \dots

Solution steps

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

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

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

= 3 - \frac{π}{3}

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