show-that-the-intergral-1-1-x-p-dx-converges-for-p-gt-1-find-it-value-

Question Number 217383 by peter frank last updated on 12/Mar/25

show that the intergral

\int_{1}^{\infty} \frac{1}{x^{p}} dx converges for p > 1

find it value

Answered by mr W last updated on 12/Mar/25

\int_{1}^{\infty} \frac{d x}{x^{p}} = {[\frac{1}{(p - 1) x^{p - 1}}]}_{\infty}^{1}

= \frac{1}{p - 1} (1 - \lim_{x \to \infty} \frac{1}{x^{p - 1}}) = \frac{1}{p - 1}

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