integral from 2y to y^2 of yzln(2)

Lösung

\int_{2 y}^{y^{2}} yz ln (2) d z

ln (2) y (\frac{y ^{4}}{2} - 2 y^{2})

Schritte zur Lösung

\int_{2 y}^{y^{2}} yz ln (2) d z

Entferne die Konstante:

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

= ln (2) y \cdot \int_{2 y}^{y^{2}} z d z

Wende die Potenzregel an

= ln (2) y [\frac{z ^{2}}{2}]_{2 y}^{y^{2}}

Berechne die Grenzen:

\frac{y ^{4}}{2} - 2 y^{2}

= ln (2) y (\frac{y ^{4}}{2} - 2 y^{2})