integral from 1 to 2 of (4-3x)^2

Lösung

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

1

Schritte zur Lösung

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

Wende U-Substitution an

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

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

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

= - (- \frac{1}{3} [\frac{u ^{3}}{3}]_{- 2}^{1})

Vereinfache

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

Berechne die Grenzen:

3

= \frac{1}{3} \cdot 3

Vereinfache

= 1

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