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 ))](Q206830.png)
$${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}} +{L}_{\mathrm{2}} ^{\mathrm{2}} } \\ $$