SOLUTION: You have a thin plate in the first quadrant of the x, y-plane. Its boundaries are {{{ y = x^2 }}} and {{{ x = y^2 }}}, and its density is ρ(x, y) = {{{ (x + 1)(y + 1) }}} g/c

Question 1041089: You have a thin plate in the first quadrant of the x, y-plane. Its boundaries are and , and
its density is ρ(x, y) = g/cm^2
(a) Set up and calculate a double integral for its area A.
(b) Set up and calculate a double integral for its mass M.
(c) Set up and calculate double integrals for its moments Mx and My of mass.
(d) Where is the center of mass of this plate?
(e) Calculate the average density of the plate.
(f) Calculate the moments of inertia , , and of the plate.
Answer by AnlytcPhil(1806) (Show Source): You can put this solution on YOUR website!
You have a thin plate in the first quadrant of the x, y-plane. Its boundaries are +y+=+x%5E2+ and +x+=+y%5E2+, and
its density is ρ(x, y) = +%28x+%2B+1%29%28y+%2B+1%29+ g/cm^2

That's too much to ask.  I'll do the first.

(a) Set up and calculate a double integral for its area A.







That's enough. The rest is a matter of setting up similar double 
integrals using the formulas in your book for moments, mass, 
average density, and moments of inertia.  Look at examples of
these in your book.  You can do it!

Edwin

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SOLUTION: You have a thin plate in the first quadrant of the x, y-plane. Its boundaries are {{{ y = x^2 }}} and {{{ x = y^2 }}}, and its density is &#961;(x, y) = {{{ (x + 1)(y + 1) }}} g/c

SOLUTION: You have a thin plate in the first quadrant of the x, y-plane. Its boundaries are {{{ y = x^2 }}} and {{{ x = y^2 }}}, and its density is ρ(x, y) = {{{ (x + 1)(y + 1) }}} g/c