integral from 0 to 1 of e^{xy}

Lösung

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

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{x} \frac{e ^{u}}{x} d u

Entferne die Konstante:

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

= \frac{1}{x} \cdot \int_{0}^{x} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Vereinfache

\frac{1}{x} [e^{u}]_{0}^{x} : \frac{[ e ^{u} ] _{0}^{x}}{x}

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

Berechne die Grenzen:

e^{x} - 1

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

\int_{- 3}^{3} (∣ x ∣ + ∣ x + 1 ∣) d x

\int_{0}^{3} 6 - 3 y^{2} d y

\int_{0}^{\frac{π}{2}} cos (sin (x)) d x

\int_{1}^{2} 3 x^{2} - 3 x + 1 d x

\int_{0}^{\frac{π}{2}} sin (x^{\frac{1}{2}}) d x