Question
evaluate the double integral
∫R∫ lny/x dA
for the region R is the rectangle defined by 1<x<e^2 and 1<y<e
∫R∫ lny/x dA
for the region R is the rectangle defined by 1<x<e^2 and 1<y<e
Answers
Steve
∫[1,e^2]∫[1,e] lny/x dy dx
= ∫[1,e^2](y/x (lny - 1))[1,e] dx
= ∫[1,e^2] [(e/x (1-1))-(1/x (0-1))] dx
= ∫[1,e^2] 1/x dx
= lnx [1,e^2]
= 2
= ∫[1,e^2](y/x (lny - 1))[1,e] dx
= ∫[1,e^2] [(e/x (1-1))-(1/x (0-1))] dx
= ∫[1,e^2] 1/x dx
= lnx [1,e^2]
= 2