integral from 0 to 2 of 10000e^{0.04x}

Lösung

\int_{0}^{2} 10000 e^{0.04 x} d x

20821.76691 \dots

Schritte zur Lösung

\int_{0}^{2} 10000 e^{0.04 x} d x

Entferne die Konstante:

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

= 10000 \cdot \int_{0}^{2} e^{0.04 x} d x

Wende U-Substitution an

= 10000 \cdot \int_{0}^{0.08} e^{u} \frac{1}{0.04} d u

Entferne die Konstante:

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

= 10000 \cdot \frac{1}{0.04} \cdot \int_{0}^{0.08} e^{u} d u

Vereinfache

= 10000 \cdot 25 \cdot \int_{0}^{0.08} e^{u} d u

Nutze das gemeinsame Integral :

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

= 10000 \cdot 25 [e^{u}]_{0}^{0.08}

Vereinfache

= 250000 [e^{u}]_{0}^{0.08}

Berechne die Grenzen:

0.08328 \dots

= 250000 \cdot 0.08328 \dots

Vereinfache

= 20821.76691 \dots

\int \frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} ( x + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{x ^{6}}{1 + x ^{12}})

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

\frac{\partial}{\partial y} (x^{2} + y^{2} - 25)

\int - 0.04 t d t