integral from 0 to 2 of 2e^x

解答

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

2 (e^{2} - 1)

十进制

12.77811 \dots

求解步骤

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

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{2} e^{x} d x

使用积分常见定则:

\int e^{x} d x = e^{x}

= 2 [e^{x}]_{0}^{2}

带入上下限计算后得:

e^{2} - 1

= 2 (e^{2} - 1)

d er i v a t i v e (3 t - 1) (2 t - 2)^{- 1}

x \to 2 lim (3 x^{2} - 4 x + 5)

\frac{\partial}{\partial z} (sin (z))

d er i v a t i v e \frac{x ^{7} + 4}{x ^{7}}

\frac{d}{d x} (\frac{5 x}{x - 1})