What is the integral from 0 to a of e^{x/a}-e^{-x/a} ?

The integral from 0 to a of e^{x/a}-e^{-x/a} is ea+(-2e+1)/e a

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

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

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

Solution steps

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

Apply the Sum Rule:

\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})

Simplify

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

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

What is the integral from 0 to a of e^{x/a}-e^{-x/a} ?
The integral from 0 to a of e^{x/a}-e^{-x/a} is ea+(-2e+1)/e a