integral from-2 to 1 of (-x^2-6x-9)

解答

\int_{- 2}^{1} (- x^{2} - 6 x - 9) d x

- 21

求解步骤

\int_{- 2}^{1} - x^{2} - 6 x - 9 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_{- 2}^{1} x^{2} d x - \int_{- 2}^{1} 6 x d x - \int_{- 2}^{1} 9 d x

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

\int_{- 2}^{1} 6 x d x = - 9

\int_{- 2}^{1} 9 d x = 27

= - 3 - (- 9) - 27

化简

= - 21

\int_{1}^{3} 2 x (x^{2} + 6) d x

\int_{1}^{3} \frac{4 ( x ^{2} + 1 )}{x ^{2}} d x

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

\int_{0}^{l o g_{5} (7)} 5^{x} d x

\int_{6 x}^{- 8} sin (t^{2}) d t