Question

Given 2 surfaces that encloses an object T, how can I obtain the bounding curves and range for T?
z=x^2+y^2 and z=-2x
I can solve for y by setting them equal x^2+y^2=-2x
I can get the z bounds by plottinng the surfaces and see whoever is on top and whoever is on the bottom.
But how can i obtain the X range?

Answer 1

I obtained the range to be -2 to 0, this was acheived by bruteforce, which is not very good of an approach

Answer 2

this is 3D, so you also want bounds on y

Answer 3

\[y=\sqrt {-{x}^{2}-2\,x}\]or \[y=-\sqrt {-{x}^{2}-2\,x}\]

Answer 4

Is the problem to find the volume?

Answer 5

FYI, here's a plot (using geogebra)

Answer 6

Kind of, I want a way to decide the ranges for each variables so it can be used to apply triple integrals to evaluate the divergence theorem and for instance the volume integral. I dont know how to find the range for x, i found it by trial and error.

\[\int\limits \!1\,{\rm d}[z={{x}^{2}+{y}^{2}\ldots -2\,x},y={- \sqrt{-{x}^{2}- 2\,x}\ldots \sqrt{-{x}^{2}-2\,x}},x={-2\ldots 0}]\]

Answer 7

Yeah that is the plot, the object T is formed by intersection of the 2 planes. I want to find out the max and min value x can take.

Thanks, and sorry for not being very proficent in describing the problem

Answer 8

Plot of object T

Answer 9

if we look at the "shadow" of the object on the x-y plane