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find-a-and-b-if-0-t-a-t-1-b-t-2-dt-converges-and-give-its-value-in-this-case-




Question Number 44475 by abdo.msup.com last updated on 29/Sep/18
find a and b  if ∫_0 ^∞  ((√t) +a(√(t+1))+b(√(t+2)))dt  converges and give its value in this case.
$${find}\:{a}\:{and}\:{b}\:\:{if}\:\int_{\mathrm{0}} ^{\infty} \:\left(\sqrt{{t}}\:+{a}\sqrt{{t}+\mathrm{1}}+{b}\sqrt{{t}+\mathrm{2}}\right){dt} \\ $$$${converges}\:{and}\:{give}\:{its}\:{value}\:{in}\:{this}\:{case}. \\ $$

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