integral from 0 to x^3 of e^{-4t}

Lösung

\int_{0}^{x^{3}} e^{- 4 t} d t

- \frac{1}{4} (e^{- 4 x^{3}} - 1)

Schritte zur Lösung

\int_{0}^{x^{3}} e^{- 4 t} d t

Wende U-Substitution an

= \int_{0}^{- 4 x^{3}} - \frac{1}{4} e^{u} d u

Entferne die Konstante:

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

= - \frac{1}{4} \cdot \int_{0}^{- 4 x^{3}} e^{u} d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{4} [e^{u}]_{0}^{- 4 x^{3}}

Berechne die Grenzen:

e^{- 4 x^{3}} - 1

= - \frac{1}{4} (e^{- 4 x^{3}} - 1)

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

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

\int_{0}^{1} 9 x^{2} - 2 x d x

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

\int_{- π}^{0} 3 cos (n x) d x