study-the-convergence-of-I-1-1-t-t-2-1-dt-in-function-of-real-Calculate-I-for-1-2-4-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 172304 by mathocean1 last updated on 25/Jun/22

study the convergence of: I(α)=∫_1 ^α (1/(t^α ((√(t^2 −1)))))dt, in function of real α. Calculate I(α) for α=1;2;4.

$${study}\:{the}\:{convergence}\:{of}: \\ $$$${I}\left(\alpha\right)=\int_{\mathrm{1}} ^{\alpha} \frac{\mathrm{1}}{{t}^{\alpha} \left(\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}\right)}{dt},\:{in}\:{function}\: \\ $$$${of}\:{real}\:\alpha. \\ $$$${Calculate}\:{I}\left(\alpha\right)\:{for}\:\alpha=\mathrm{1};\mathrm{2};\mathrm{4}.\: \\ $$

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