integral from 1 to y of y/x

Lösung

\int_{1}^{y} \frac{y}{x} d x

y ln ∣ y ∣

Schritte zur Lösung

\int_{1}^{y} \frac{y}{x} d x

Entferne die Konstante:

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

= y \cdot \int_{1}^{y} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= y [ln ∣ x ∣]_{1}^{y}

Berechne die Grenzen:

ln ∣ y ∣

= y ln ∣ y ∣

\int_{3}^{4.3} (12 x^{2} - 6 x + 4) d x

\int_{1}^{3} \frac{1}{2} d x

\int_{3}^{6} (x^{2} - 6 x + 9) d x

\int_{0}^{l n (A)} 9 e^{3 x} d x

\int_{1}^{2} \frac{x}{3} d x