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

Lösung

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

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

Dezimale

3.40752 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

= 2 [e^{u} u - e^{u}]_{1}^{2}

Berechne die Grenzen:

2 e^{2} - e^{2}

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

\int_{0}^{4} \frac{1}{4 x ^{2} + 25} d x

\int_{0}^{\infty} x e^{- \frac{x}{θ}} d x

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

\int_{\frac{1}{3}}^{3} \frac{1}{4 x} d x

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