Volume integral with 3 formulas mmn 15 3a

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SUMMARY

The discussion centers on finding the volume enclosed by the surfaces defined by the equations z=0, x=y, and y²+z²=x. Participants emphasize the importance of visualizing the shape formed by these equations, particularly the challenges of projecting onto the x-y plane and understanding the resulting geometry. The inability to accurately imagine the paraboloid intersecting the x=0 and z=0 planes is a key obstacle in solving the volume integral. Effective visualization techniques and projection methods are essential for resolving this problem.

PREREQUISITES
  • Understanding of volume integrals in multivariable calculus
  • Familiarity with the equations of surfaces in three-dimensional space
  • Knowledge of projection techniques in geometry
  • Ability to visualize three-dimensional shapes from two-dimensional projections
NEXT STEPS
  • Study the properties of paraboloids and their intersections with planes
  • Learn techniques for visualizing three-dimensional shapes from two-dimensional projections
  • Explore volume integration methods in multivariable calculus
  • Investigate software tools for 3D graphing, such as GeoGebra or MATLAB
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus and geometry, as well as educators seeking to enhance their teaching methods for visualizing complex shapes.

nhrock3
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find the volume inclosed by z=0 x=y and y^2+z^2=x
??

i am having trouble drawing it
i know i should look on th shadow of it on the x-y plane and integrate by it

i can project on every plane i want to and build the integral appropriatly
i jast can't imagine this shape

if i can find out how the shape looks like
then it will solve it very fast
but imaganening a parabaloid cutting x=0 plane and z=0
is very hard thing to draw and imagine
 
Physics news on Phys.org
Tell us what you get when you project onto each plane?
 
thats the problem i don't know how to draw it
 

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