integral from 0 to y of xyz

Lösung

\int_{0}^{y} x yz d x

\frac{y ^{3} z}{2}

Schritte zur Lösung

\int_{0}^{y} x yz d x

Entferne die Konstante:

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

= yz \cdot \int_{0}^{y} x d x

Wende die Potenzregel an

= yz [\frac{x ^{2}}{2}]_{0}^{y}

Berechne die Grenzen:

\frac{y ^{2}}{2}

= yz \frac{y ^{2}}{2}

Vereinfache

= \frac{y ^{3} z}{2}

\int_{2}^{5} cos (\frac{x}{10}) d x

\int_{1}^{5} (3 x^{2} + 4 x + 1) d x

\int_{3}^{5} 6 x^{2} (x^{3} + 4)^{3} d x

\int_{0}^{7} - x^{2} + 7 x d x

\int_{0}^{t} 20 t e^{- 10 t} d t