integral from-1 to 3 of (-3x^2+8x+5)

解答

\int_{- 1}^{3} (- 3 x^{2} + 8 x + 5) d x

24

求解步骤

\int_{- 1}^{3} - 3 x^{2} + 8 x + 5 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_{- 1}^{3} 3 x^{2} d x + \int_{- 1}^{3} 8 x d x + \int_{- 1}^{3} 5 d x

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} 8 x d x = 32

\int_{- 1}^{3} 5 d x = 20

= - 28 + 32 + 20

化简

= 24

\int_{- 1}^{1} 8^{x} d x

\int_{0}^{6} x^{2} - 6 x + 5 d x

\int_{- 1}^{1} (y^{2} - 7) - (e^{y}) d y

\int_{0}^{1} \frac{1}{5 x - 10} d x

\int_{0}^{x} t^{3} d t