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

解答

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

3 - \frac{π}{3}

十进制

0.68485 \dots

求解步骤

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

使用积分加法定则:

\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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