integral from 0 to ln(2) of e^{5x}

Lösung

\int_{0}^{l n (2)} e^{5 x} d x

\frac{31}{5}

Dezimale

6.2

Schritte zur Lösung

\int_{0}^{l n (2)} e^{5 x} d x

Wende U-Substitution an

= \int_{0}^{5 l n (2)} e^{u} \frac{1}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{0}^{5 l n (2)} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{5} [e^{u}]_{0}^{5 l n (2)}

Berechne die Grenzen:

31

= \frac{1}{5} \cdot 31

Vereinfache

= \frac{31}{5}

\int_{0}^{6} x^{2} - 4 d x

\int_{- 2}^{3} (6 x^{2} - 5) d x

\int_{0}^{40} x^{2} + 10 x - 90 d x

\int_{1}^{5} 3 x^{2} d x

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