integral from 1 to 2 of (11-10x)^4

Lösung

\int_{1}^{2} (11 - 10 x)^{4} d x

1181

Schritte zur Lösung

\int_{1}^{2} (11 - 10 x)^{4} d x

Wende U-Substitution an

= \int_{1}^{- 9} - \frac{u ^{4}}{10} d u

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

= - \int_{- 9}^{1} - \frac{u ^{4}}{10} d u

Entferne die Konstante:

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

= - (- \frac{1}{10} \cdot \int_{- 9}^{1} u^{4} d u)

Wende die Potenzregel an

= - (- \frac{1}{10} [\frac{u ^{5}}{5}]_{- 9}^{1})

Vereinfache

= \frac{1}{10} [\frac{u ^{5}}{5}]_{- 9}^{1}

Berechne die Grenzen:

11810

= \frac{1}{10} \cdot 11810

Vereinfache

= 1181

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