integral from 1 to 8 of 1/(x^p)

Lösung

\int_{1}^{8} \frac{1}{x ^{p}} d x

\frac{8 ^{- p + 1} - 1}{- p + 1}

Schritte zur Lösung

\int_{1}^{8} \frac{1}{x ^{p}} d x

Wende die Potenzregel an

= [\frac{x ^{- p + 1}}{- p + 1}]_{1}^{8}

Berechne die Grenzen:

\frac{8 ^{- p + 1}}{- p + 1} - \frac{1}{- p + 1}

= \frac{8 ^{- p + 1}}{- p + 1} - \frac{1}{- p + 1}

Vereinfache

= \frac{8 ^{- p + 1} - 1}{- p + 1}

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