integral from 0 to t of xe^{-x}

Lösung

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

- t e^{- t} - e^{- t} + 1

Schritte zur Lösung

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

Wende die partielle Integration an

= [- e^{- x} x - \int - e^{- x} d x]_{0}^{t}

\int - e^{- x} d x = e^{- x}

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

Berechne die Grenzen:

- t e^{- t} - e^{- t} + 1

= - t e^{- t} - e^{- t} + 1

x y^{^{'}} - y = 2 x^{2} - 2 x - 2

x y^{^{'}} - y = x, y (1) = 10

\int_{0}^{2} π (3 x^{2})^{2} d x

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{4})

x \to 1 - lim (\frac{1}{x} - 1)