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

Lösung

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

- e^{- x} + 1

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= - [e^{u}]_{0}^{- x}

Berechne die Grenzen:

e^{- x} - 1

= - (e^{- x} - 1)

Vereinfache

= - e^{- x} + 1

\int_{- \frac{3}{2}}^{\frac{3}{2}} x^{3} - x + 2 d x

\int_{- 2}^{2} x (x^{2} - 9) d x

\int_{0}^{2} (x^{3} + 4 x) d x

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

\int_{0}^{2} x 1 + 4 x^{2} d x