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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.
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