integral from 1 to 2 of 4e^{2x}

Lösung

\int_{1}^{2} 4 e^{2 x} d x

2 (e^{4} - e^{2})

Dezimale

94.41818 \dots

Schritte zur Lösung

\int_{1}^{2} 4 e^{2 x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{2} e^{2 x} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

4 \cdot \frac{1}{2} [e^{u}]_{2}^{4} : 2 [e^{u}]_{2}^{4}

= 2 [e^{u}]_{2}^{4}

Berechne die Grenzen:

e^{4} - e^{2}

= 2 (e^{4} - e^{2})

\int_{8}^{10} x (x^{2} - 64)^{2} d x

\int_{0}^{1} x sin (x y) d y

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

\int_{0}^{x^{3}} sin (\frac{y}{x}) d y

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