Patience, please.Timebomb3750 said:Any assistance would be greatly appreciated. Thanks.
Timebomb3750 said:Homework Statement
Use a triple integral to find the volume of the region. Below x+2y+2z=4, above z=2x, in the first octant.
Homework Equations
V=∫∫∫dV=∫∫∫dxdydz
The Attempt at a Solution
I have no clue where to begin as to finding those darn limits to integrate with. I'm sure I can evaluate the integral just fine, but I need help finding limits.
Where do the planes, x+2y+2z=4, and, z=2x, intersect?Timebomb3750 said:Well, after plotting those two equations into my mac grapher app, it seems my y-limits could be from 0 to 2. But I'm unsure as to finding my x and z limits.
SammyS said:Where do the planes, x+2y+2z=4, and, z=2x, intersect?
Where does each of those planes intersect the coordinate axes?
I should have asked, "Where does each of those planes intersect the coordinate planes?"Timebomb3750 said:Well, z=2x goes through the entire the y-axis, but doesn't intersect any other axes. x+2y+2z=4 intersects axes at x=4, y=2, and z=2.
The two planes intersect at 2y+5x=4.
But what's your point? What do I get out of this?
A triple integral is an integral that integrates a three-dimensional function over a region in three-dimensional space.
Triple integrals are used when dealing with three-dimensional objects or functions, such as finding the volume of a solid or the mass of a three-dimensional object.
To set up a triple integral, you need to define the limits of integration for each variable (x, y, and z) and determine the correct order of integration based on the shape of the region being integrated over.
Triple integrals have various applications in physics, engineering, and other fields. They are commonly used to find the mass, center of mass, and moment of inertia of a three-dimensional object, as well as to calculate the volume of a solid bounded by surfaces.
Triple integrals can be challenging to set up and evaluate, as they require a good understanding of three-dimensional geometry and calculus. Additionally, the limits of integration can be difficult to determine for complex regions. Using computer software or graphing tools can help with these challenges.