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.


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

$s t u d y t h e c o n v e r g e n c e o f :$ $I (α) = \int_{1}^{α} \frac{1}{t^{α} (\sqrt{t^{2} - 1})} d t, i n f u n c t i o n$ $o f r e a l α .$ $C a l c u l a t e I (α) f o r α = 1; 2; 4 .$
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