integral from 0 to 3 of x^3-2x^2-3x

解答

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

- \frac{45}{4}

十进制

- 11.25

求解步骤

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

\int_{0}^{3} x^{3} d x = \frac{81}{4}

\int_{0}^{3} 2 x^{2} d x = 18

\int_{0}^{3} 3 x d x = \frac{27}{2}

= \frac{81}{4} - 18 - \frac{27}{2}

化简

\frac{81}{4} - 18 - \frac{27}{2} : - \frac{45}{4}

= - \frac{45}{4}

\int_{- 2}^{4} (x - 1)^{2} d x

\int_{1}^{4} (32 x + 14) d x

\int_{3}^{4} x^{3} - π x^{2} d x

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

\int_{0}^{1} (4 x + 7) d x