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

解答

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

\frac{3}{2} + \frac{π}{3}

十进制

1.91322 \dots

求解步骤

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

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

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

= \frac{3}{2} + \frac{π}{3}

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