integral from 1 to 0 of 2x+3

解答

\int_{1}^{0} 2 x + 3 d x

- 4

求解步骤

\int_{1}^{0} 2 x + 3 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} 2 x + 3 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}^{1} 2 x d x + \int_{0}^{1} 3 d x)

\int_{0}^{1} 2 x d x = 1

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

= - (1 + 3)

化简

= - 4