integral from 0 to 1 of (e^{2x})

Lösung

\int_{0}^{1} (e^{2 x}) d x

\frac{e ^{2} - 1}{2}

Dezimale

3.19452 \dots

Schritte zur Lösung

\int_{0}^{1} e^{2 x} d x

Wende U-Substitution an

= \int_{0}^{2} 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_{0}^{2} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{0}^{2}

Berechne die Grenzen:

e^{2} - 1

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

Vereinfache

= \frac{e ^{2} - 1}{2}

\int_{0}^{1} (3 x^{e} + 4 e^{x}) d x

\int_{0}^{16} t d t

\int_{1}^{3} sin (z^{2}) d z

\int_{k}^{x} \frac{1}{t} d t

\int_{0}^{1} \frac{x - 1}{x} d x