- #1
WannaBe22
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Homework Statement
Hey there, I'll be delighted to get some help in the following question:
Let A be the region in space bounded by the next planes:
[tex] x=1[/tex], [tex]x=2[/tex], [tex]x-y+1=0[/tex],
[tex]x-2y=2[/tex], [tex]x+y-z=0[/tex] , [tex]z=0[/tex]...
Write the integral [tex] \int \int \int_{A} f(x,y,z) dxdydz [/tex] as shown in the theorem above.
The problem is I can't figure out how the region A looks like...
Hope you'll be able to help me dealing with this question...
Thanks in advance
Homework Equations
Let E be a closed region with a surface in R^2 and let [tex] g^1, g^2[/tex] be two real functions, continuous in E. Let's look at A:
[tex] A=( (x,y,z)|(x,y) \in E, g^1(x,y)\leq z \leq g^2(x,y) [/tex]. Then if f is a continuous function with 3 variables, continuous in A, then:
[tex] \int \int \int_{A} f(x,y,z) dxdydz = \int \int_{E} (\int_{g^1(x,y)}^{g^2(x,y)} f(x,y,z)dz) dxdy [/tex]...