Calculating Volume of 3D Region in 1st Octant

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SUMMARY

The discussion focuses on calculating the volume of a 3D region in the first octant, specifically bounded by the coordinate planes and the planes defined by the equations x + z = 1 and y + 2x = 2. Participants emphasize the necessity of visualizing the region through sketching to facilitate understanding. The use of a triple integral is suggested as the appropriate mathematical tool for solving the volume calculation, although the initial poster expresses uncertainty about how to begin the problem-solving process.

PREREQUISITES
  • Understanding of triple integrals in calculus
  • Familiarity with the concept of bounded regions in three-dimensional space
  • Basic knowledge of coordinate planes and their equations
  • Ability to sketch 3D geometric shapes
NEXT STEPS
  • Study the application of triple integrals for volume calculations
  • Learn how to visualize and sketch 3D regions defined by equations
  • Explore the method of setting up integrals for bounded regions
  • Review examples of volume calculations in the first octant
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable calculus and volume calculations, as well as educators seeking to enhance their teaching methods for geometric interpretations in mathematics.

jimbo71
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Homework Statement



the region in the first octant bounded by the coordinate planes and the planes x+z=1, y+2x=2


Homework Equations


triple integral or region R dzdxdy?

The Attempt at a Solution


i need a lot of help for this problem
 
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Hi jimbo71,

You won't get any help if you don't show an attempt.
 
i don't know where to start!
 
Start by drawing a picture of the region.
 

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