integral from 4 to 2 of 2x

Lösung

\int_{4}^{2} 2 x d x

- 12

Schritte zur Lösung

\int_{4}^{2} 2 x d x

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

= - \int_{2}^{4} 2 x d x

Entferne die Konstante:

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

= - 2 \cdot \int_{2}^{4} x d x

Wende die Potenzregel an

= - 2 [\frac{x ^{2}}{2}]_{2}^{4}

Berechne die Grenzen:

6

= - 2 \cdot 6

Vereinfache

= - 12

\int_{0}^{3} (t^{2} - 2 t) d t

\int_{0}^{1} e^{3 y} d y

\int_{- 5}^{5} \frac{9}{x ^{3}} d x

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

\int_{- 2}^{3} e^{\frac{- 4 x}{3}} d x