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c-a-0-a-1-1-f-x-2-dx-2-b-0-b-1-1-f-x-2-dx-2-c-L-1-2-L-2-2-




Question Number 206830 by Fabricista15 last updated on 27/Apr/24
c = (√((∫_a_0  ^a_1  (√(1+[f′(x)]^2 ))dx)^2 +(∫_b_0  ^b_1  (√(1+[f′(x)]^2 ))dx)^2 ))  c = (√(L_1 ^2 +L_2 ^2 ))
$${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}} +{L}_{\mathrm{2}} ^{\mathrm{2}} } \\ $$

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