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let-give-I-n-1-n-1-1-t-2-dt-1-calculate-I-n-2-find-lim-n-I-n-




Question Number 31466 by abdo imad last updated on 08/Mar/18
let give I_n = āˆ«_(1/n) ^1  (āˆš(1+t^2 )) dt  1) calculate I_n   2) find lim_(nā†’āˆž)  I_n    .
$${let}\:{give}\:{I}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{I}_{{n}} \:\:\:. \\ $$

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