Multiple Integrals Anyone? Find the volume of the region bounded on top by the plane z=x+3y+1, on the bottom by the plane z=1/10(x(^2)+y(^2)), and on the sides by the planes x=0, x=3, y=1, y=2.

Question

perl · Answer

do you know the process

perl · Answer

first graph the region

phi · Answer

on the bottom by the plane z=1/10(x(^2)+y(^2))  

is a paraboloid shape

perl · Answer

so thats not a plane, theres a typo in the question

perl · Answer

Find the volume of the region bounded on top by the plane z=x+3y+1, on the bottom by the *surface* z=1/10(x(^2)+y(^2)), and on the sides by the planes x=0, x=3, y=1, y=2.

perl · Answer

you can do an idea similiar in one variable calculus, where integrate f(x) - g(x) ,

anonymous · Answer

I just don't know how to set up the problem. I understand how to integrate with the multiple variables but I don't know what to do with the top and bottom equations.

perl · Answer

first graph the region over which you will integrate

perl · Answer

ok took me a while to find your question

perl · Answer

im trying to get the draw button to work

anonymous · Answer

So do I subtract the two functions of the top and bottom surfaces? $$\int\limits_{0}^{3}\int\limits_{1}^{2}f(x,y)-g(x,y) dx dy$$

perl · Answer

you have the limits backwards though

perl · Answer

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