Question: Problem 4. The area of a surface given by the equationz=f(x,y)for (x,y)inD, where Dis a domain in the xy-plane, can be determined using the surfacearea

Problem 4. The area of a surface given by the equationz=f(x,y)for (x,y)inD, where Dis a domain in the xy-plane, can be determined using the surfacearea integral:A(S)=D1+|gradf|22dA.Let f(x,y)be the upper hemisphere of the sphere:x2+y2+z2=4,z>0where (x,y) lie in the disk:D:,x2+y2-2y0.Determine the area of the surface S defined byf(x,y) over the domain D.

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