integral from 0 to 1 of (-x^2-3x)

解答

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

- \frac{11}{6}

十进制

- 1.83333 \dots

求解步骤

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 3 x d x = \frac{3}{2}

= - \frac{1}{3} - \frac{3}{2}

化简

- \frac{1}{3} - \frac{3}{2} : - \frac{11}{6}

= - \frac{11}{6}

\int_{- 5}^{5} (5 + 25 - x^{2}) d x

\int_{0}^{1 - y^{2}} c x d x

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

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

\int_{0}^{9} 2 t d t