integral from 0 to 5 of 2e^x

Lösung

\int_{0}^{5} 2 e^{x} d x

2 (e^{5} - 1)

Dezimale

294.82631 \dots

Schritte zur Lösung

\int_{0}^{5} 2 e^{x} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{5} e^{x} d x

Nutze das gemeinsame Integral :

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

= 2 [e^{x}]_{0}^{5}

Berechne die Grenzen:

e^{5} - 1

= 2 (e^{5} - 1)

x \to 2 lim (3 x^{3} + 5 x)

x \to \frac{π}{2} lim (4 sin (x))

x \to 1 - lim (\frac{x + 2}{1 - x})

t an g e n t f (x) = 5 x^{2} - 2 x, at x = 3

d er i v a t i v e f (x) = \frac{1}{2} x^{3} - 2 x + 3