integral from-infinity to 0 of e^xx

解答

\int_{- \infty}^{0} e^{x} x d x

- 1

求解步骤

\int_{- \infty}^{0} e^{x} x d x

计算不定积分:

\int e^{x} x d x = e^{x} x - e^{x} + C

带入上下限计算后得:

\int_{- \infty}^{0} e^{x} x d x = - 1 - 0

= - 1 - 0

化简

= - 1

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

\int_{- 5}^{5} 3 x d x

\int_{25}^{x} \frac{1}{t} d t

\int_{- 1}^{8} (x^{\frac{1}{3}} - x) d x

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