integral from 1 to 2 of (2x-1)^3

Lösung

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

10

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{3} \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{3} u^{3} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{4}}{4}]_{1}^{3}

Berechne die Grenzen:

20

= \frac{1}{2} \cdot 20

Vereinfache

= 10

\int_{0}^{1} x 1 + x d x

\int_{0}^{1} \frac{x + y}{z} d x

\int_{- 1}^{3} (3 u - 8) (u + 3) d u

\int_{0}^{2} 1 + e^{2 x} d x

\int_{1}^{4} ∣ 3 x - 9 ∣ d x