integral from x to 0 of e^{-10t}

Lösung

\int_{x}^{0} e^{- 10 t} d t

- \frac{1}{10} (1 - e^{- 10 x})

Schritte zur Lösung

\int_{x}^{0} e^{- 10 t} d t

Wende U-Substitution an

= \int_{- 10 x}^{0} - \frac{1}{10} e^{u} d u

Entferne die Konstante:

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

= - \frac{1}{10} \cdot \int_{- 10 x}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{10} [e^{u}]_{- 10 x}^{0}

Berechne die Grenzen:

1 - e^{- 10 x}

= - \frac{1}{10} (1 - e^{- 10 x})

\int_{0}^{1} cos (w x) d x

\int_{- 2}^{3} (9 - x^{2}) - (3 - x) d x

\int_{0}^{x^{3}} e^{- 2 t} d t

\int_{3}^{7} x^{2} lo g_{10} (x) d x

\int_{6}^{9} (\frac{1}{x ^{2}}) d x