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## Homework Statement

∫∫

_{s}x √(y

^{2}+ 4) where S: y

^{2}+ 4z = 16, and portion cut by planes x=0, x=1, z=0.

## Homework Equations

I attempted to solve using the surface area integral formula, whereby this double integral is transformed to ∫∫f(x,y,g(x,y)) √((∂z/∂x)

^{2}+ (∂z/∂y)

^{2}+ 1) dA

## The Attempt at a Solution

Solving for z in the S region, and finding partials with respect to x and y yields A(S) of √(1+(1/4)y

^{2}) which can be rewritten as 1/2 √(4+y

^{2})

Multiplying this by the original function, which is a function of just x and y, gives ∫∫ x/2*(4 + y

^{2}) dA.

I'm having trouble finding the limits of integration for the given planes.