integral from 0 to a of e^{x/a}-e^{-x/a}

解答

\int_{0}^{a} e^{\frac{x}{a}} - e^{- \frac{x}{a}} d x

e a + \frac{- 2 e + 1}{e} a

求解步骤

\int_{0}^{a} e^{\frac{x}{a}} - e^{- \frac{x}{a}} 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}^{a} e^{\frac{x}{a}} d x - \int_{0}^{a} e^{- \frac{x}{a}} d x

\int_{0}^{a} e^{\frac{x}{a}} d x = a (e - 1)

\int_{0}^{a} e^{- \frac{x}{a}} d x = a (1 - \frac{1}{e})

= a (e - 1) - a (1 - \frac{1}{e})

化简

a (e - 1) - a (1 - \frac{1}{e}) : e a + \frac{- 2 e + 1}{e} a

= e a + \frac{- 2 e + 1}{e} a

d er i v a t i v e x = 6.4 sin (1. 2^{2} t^{2})

\frac{\partial ^{2}}{\partial x \partial y} (x^{5} + x^{2} y + x + 3)

d er i v a t i v e - 7

\int cos (30 x) \cdot cos (4 x) \cdot cos (4 x) d x

y^{^{'}} = x + y, y (0) = 10