integral from 2 to 0 of cx

Lösung

\int_{2}^{0} c x d x

- c \cdot 2

Schritte zur Lösung

\int_{2}^{0} c x d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{2} c x d x

Entferne die Konstante:

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

= - c \cdot \int_{0}^{2} x d x

Wende die Potenzregel an

= - c [\frac{x ^{2}}{2}]_{0}^{2}

Berechne die Grenzen:

2

= - c \cdot 2

\int_{0}^{1} \frac{2}{x ^{3}} d x

\int_{0}^{1} - \frac{( x - 1 ) ^{3}}{3} d x

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

\int_{- 4}^{0} (- x^{2} - 4 x) d x

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