integral from 0 to 2 of 30000e^{0.03x}

Lösung

\int_{0}^{2} 30000 e^{0.03 x} d x

61836.54654 \dots

Schritte zur Lösung

\int_{0}^{2} 30000 e^{0.03 x} d x

Entferne die Konstante:

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

= 30000 \cdot \int_{0}^{2} e^{0.03 x} d x

Wende U-Substitution an

= 30000 \cdot \int_{0}^{0.06} e^{u} \frac{1}{0.03} d u

Entferne die Konstante:

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

= 30000 \cdot \frac{1}{0.03} \cdot \int_{0}^{0.06} e^{u} d u

Vereinfache

= 30000 \cdot 33.33333 \dots \cdot \int_{0}^{0.06} e^{u} d u

Nutze das gemeinsame Integral :

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

= 30000 \cdot 33.33333 \dots [e^{u}]_{0}^{0.06}

Vereinfache

= 1000000 [e^{u}]_{0}^{0.06}

Berechne die Grenzen:

0.06183 \dots

= 1000000 \cdot 0.06183 \dots

Vereinfache

= 61836.54654 \dots

\int 36 t^{8} e^{- t^{9}} d t

x \to - 1 lim (5 - 11 x)

t an g e n t x^{2} + 5

\frac{d}{d x} (\frac{x ^{3}}{3} + 7 x^{2} + 50 x)

\frac{\partial}{\partial x} (5 arccot (x))