Where Can I Find Resources to Help Me Solve Double Integral Problems?

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Homework Help Overview

The discussion revolves around setting up a double integral to find the volume of a solid bounded by a cylinder and several planes. The problem involves understanding the geometric constraints imposed by the cylinder defined by y² + z² = 9 and the planes x = 0, y = 0, z = 0, and 2x + y = 2.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss how to set up the double integral and find the limits of integration. There are suggestions to sketch the solid to better visualize the integration region. Some participants also question the definitions of the planes mentioned in the problem statement.

Discussion Status

The discussion is ongoing, with several participants providing hints and suggestions for approaching the problem. There is acknowledgment of the difficulty in setting up the integral, and some guidance has been offered regarding the order of integration. However, there is no explicit consensus on the setup yet.

Contextual Notes

Some participants note potential confusion regarding the description of the planes, specifically clarifying that x = 0, y = 0, z = 0 refers to the coordinate planes rather than individual planes. There is also mention of external resources that may not be directly relevant to the problem at hand.

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Homework Statement


Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.

Homework Equations


None.

The Attempt at a Solution


This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?
 
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Math10 said:

Homework Statement


Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.

Homework Equations


None.

The Attempt at a Solution


This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?
Setting these integrals up is often the hardest part. Have you drawn a sketch of the solid?
 
Math10 said:

Homework Statement


Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.

Homework Equations


None.

The Attempt at a Solution


This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?

Please show you solution efforts. However, to help you start, here is a hint: when doing double or triple integral problems, always, always, always make a sketch of the integration region. It will help you figure out what your next steps should be.
 
You can write z in terms of y and x in terms of y, so I would recommend y be your outer integral. Neither z nor x depend on each other, so their order should not matter.
 
You need to setup the integral and then you'll know how to setup the limits.

There are some videos on the mathispower4u that talk about the washer method and the shell method:

https://dl.dropboxusercontent.com/u/28928849/Webpages/Calculus2VideoLibraryTable.htm
 
jedishrfu said:
You need to setup the integral and then you'll know how to setup the limits.

There are some videos on the mathispower4u that talk about the washer method and the shell method:
Neither of which is relevant to this problem.
 
Math10 said:
Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.
x=0, y=0, z=0 isn't a plane, it is a point. I expect you mean the plane y=0, z=0.
 
Svein said:
x=0, y=0, z=0 isn't a plane, it is a point. I expect you mean the plane y=0, z=0.

No, that is the three coordinate planes. He wrote what he meant there.
 
LCKurtz said:
No, that is the three coordinate planes. He wrote what he meant there.
Ah. Sorry.
 
  • #10
LCKurtz said:
Neither of which is relevant to this problem.

Yes that's true but the real point of the post was to tell the OP about a resource that would help him which was located near these references.
 

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