integral from 5 to 10 of ((5-x)^4)/(625)

Lösung

\int_{5}^{10} \frac{( 5 - x ) ^{4}}{625} d x

1

Schritte zur Lösung

\int_{5}^{10} \frac{( 5 - x ) ^{4}}{625} d x

Entferne die Konstante:

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

= \frac{1}{625} \cdot \int_{5}^{10} (5 - x)^{4} d x

Wende U-Substitution an

= \frac{1}{625} \cdot \int_{0}^{- 5} - u^{4} d u

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

= \frac{1}{625} (- \int_{- 5}^{0} - u^{4} d u)

Entferne die Konstante:

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

= \frac{1}{625} (- (- \int_{- 5}^{0} u^{4} d u))

Wende die Potenzregel an

= \frac{1}{625} (- (- [\frac{u ^{5}}{5}]_{- 5}^{0}))

Vereinfache

= \frac{1}{625} [\frac{u ^{5}}{5}]_{- 5}^{0}

Berechne die Grenzen:

625

= \frac{1}{625} \cdot 625

Vereinfache

= 1

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