integral from 0 to 1 of e^{-x}-e^x

Lösung

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

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

Dezimale

- 1.08616 \dots

Schritte zur Lösung

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

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

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

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

Vereinfache

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

\int_{0}^{1} 2 π x (x - x^{4}) d x

\int_{- 1}^{1} (y^{2} - 2 - e^{y}) d y

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

\int_{0}^{2} 2 t^{2} d t

\int_{1}^{3} 2 x^{2} e^{x^{3}} d x