integral from 3 to 5 of-x^2+8x-12

解答

\int_{3}^{5} - x^{2} + 8 x - 12 d x

\frac{22}{3}

十进制

7.33333 \dots

求解步骤

\int_{3}^{5} - x^{2} + 8 x - 12 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_{3}^{5} x^{2} d x + \int_{3}^{5} 8 x d x - \int_{3}^{5} 12 d x

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 8 x d x = 64

\int_{3}^{5} 12 d x = 24

= - \frac{98}{3} + 64 - 24

化简

- \frac{98}{3} + 64 - 24 : \frac{22}{3}

= \frac{22}{3}

\int_{2}^{8} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\int_{1}^{2} (\frac{2}{x} - e^{3 x}) d x

\int_{1}^{2} 8 \cdot e^{4 x - 3} d x

\int_{0}^{x^{2}} t d t

\int_{- 1}^{2} x^{3} - 2 x^{2} - 5 x + 6 d x