neutrino said:Are sure that the equation is linear in all the variables?
Thanks...I'll have to straighten out my terminology. I just wanted to convey the fact that the given equation did not represent a solid.HallsofIvy said:I don't understand that question: first, being linear is not really relevant to the problem (it just makes the integration easier) and, second, yes, it clearly is linear in all variables!
However, denien, I would point out that [itex]\frac{x}{3}+ \frac{y}{4}+ \frac{z}{5}= 1[/itex] is not a solid! It may well give one boundary of a solid but where are the others? (Possibly the coordinate planes?)
The region of integration for a function in two variables refers to the area in the xy-plane over which the function is being integrated. It is represented by a closed region bounded by curves, lines, or a combination of both.
To determine the limits of integration, you can start by sketching the region and identifying its boundaries. Then, determine the equations of those boundaries and find their intersection points. The limits of integration will be the x and y values of those intersection points.
Yes, the region of integration can be non-rectangular. It can take various shapes such as triangles, circles, or irregular polygons. The important thing is to accurately identify the boundaries of the region and set up the limits of integration accordingly.
The purpose of finding the region of integration is to accurately set up the limits of integration for a double integral. This allows us to evaluate the integral and find the volume under the surface defined by the function.
Yes, there are various techniques for finding the region of integration such as using symmetry, setting up the region as a Type I or Type II region, and using polar coordinates. The choice of technique depends on the shape and complexity of the region.