integral from-1 to 1 of (y^2-4)-(e^y)

Lösung

\int_{- 1}^{1} (y^{2} - 4) - (e^{y}) d y

- e + \frac{1}{e} - \frac{22}{3}

Dezimale

- 9.68373 \dots

Schritte zur Lösung

\int_{- 1}^{1} y^{2} - 4 - e^{y} d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{1} y^{2} d y - \int_{- 1}^{1} 4 d y - \int_{- 1}^{1} e^{y} d y

\int_{- 1}^{1} y^{2} d y = \frac{2}{3}

\int_{- 1}^{1} 4 d y = 8

\int_{- 1}^{1} e^{y} d y = e - \frac{1}{e}

= \frac{2}{3} - 8 - (e - \frac{1}{e})

Vereinfache

\frac{2}{3} - 8 - (e - \frac{1}{e}) : - e + \frac{1}{e} - \frac{22}{3}

= - e + \frac{1}{e} - \frac{22}{3}

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

\int_{0}^{9} x^{2} - 4 d x

\int_{- 2}^{3} (x + 2) - (x^{2} - 4) d x

\int_{0}^{2} 12 d x

\int_{0}^{5} 2 t e^{- t^{2}} d t