integral from 0 to 4 of x^2*x/8

Lösung

\int_{0}^{4} x^{2} \cdot \frac{x}{8} d x

8

Schritte zur Lösung

\int_{0}^{4} x^{2} \frac{x}{8} d x

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{0}^{4} x^{2} x d x

Vereinfache

x^{2} x : x^{3}

= \frac{1}{8} \cdot \int_{0}^{4} x^{3} d x

Wende die Potenzregel an

= \frac{1}{8} [\frac{x ^{4}}{4}]_{0}^{4}

Berechne die Grenzen:

64

= \frac{1}{8} \cdot 64

Vereinfache

= 8

\int_{0}^{4} 2 π x (2 x) d x

\int_{0}^{x^{4}} e^{- 2 t} d t

\int_{1}^{2} \frac{1}{x} - \frac{x}{4} d x

\int_{1}^{8} \frac{10}{x} d x

\int_{- 1}^{b} x^{2} (7 - x) d x