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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summenregel an:

\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})

Vereinfache

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

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

Beliebte Beispiele

derivative x=6.4sin(1.2^2t^2)

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

(\partial ^2)/(\partial x\partial y)(x^5+x^2y+x+3)

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

d er i v a t i v e - 7

integral of cos(30x)*cos(4x)*cos(4x)

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

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

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