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Beliebt Rechnen >

integral from 0 to 33 of 3(x-1)^{-1/5}

Lösung

\int_{0}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

Lösung

\frac{225}{4}

+1

Dezimale

56.25

Schritte zur Lösung

\int_{0}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 1

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{1} 3 (x - 1)^{- \frac{1}{5}} d x + \int_{1}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

\int_{0}^{1} 3 (x - 1)^{- \frac{1}{5}} d x = - \frac{15 ( - 1 ) ^{\frac{4}{5}}}{4}

\int_{1}^{33} 3 (x - 1)^{- \frac{1}{5}} d x = 60

= - \frac{15 ( - 1 ) ^{\frac{4}{5}}}{4} + 60

Vereinfache

- \frac{15 ( - 1 ) ^{\frac{4}{5}}}{4} + 60 : \frac{225}{4}

= \frac{225}{4}

Graph

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