integral from 2 to 4 of e^{2x}

Lösung

\int_{2}^{4} e^{2 x} d x

\frac{e ^{8} - e ^{4}}{2}

Dezimale

1463.17991 \dots

Schritte zur Lösung

\int_{2}^{4} e^{2 x} d x

Wende U-Substitution an

= \int_{4}^{8} e^{u} \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{4}^{8} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{4}^{8}

Berechne die Grenzen:

e^{8} - e^{4}

= \frac{1}{2} (e^{8} - e^{4})

Vereinfache

= \frac{e ^{8} - e ^{4}}{2}

\int_{\frac{1}{2}}^{1} x (e - e^{x}) d x

\int_{- 1}^{1} (x^{3} - \frac{3 x}{5})^{2} d x

\int_{0}^{1} 8 x^{2} + 1 d x

\int_{x}^{1} 6 x yz d z

\int_{0}^{2} 1