Need help volume calculation .

In summary, the problem with my attempt to solve it is that I did not have the limits of integration on u and v. I had the limits of integration on z, but it was difficult to solve symbolically.
  • #1
sedaw
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0
attached herewith : the problem with my attempt to solve it .
 

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  • #2
1. What is "an" in "cot ant"?

2. How did you get the limits of integration? Specifically, what are the limits of integration on u and v?
 
  • #3
HallsofIvy said:
1. What is "an" in "cot ant"?

2. How did you get the limits of integration? Specifically, what are the limits of integration on u and v?

cotan(t) = cos(t)/sit(t)

the limits of integration on u & v simply received from the projection of the region bounded by V on the UV plane -> you can see it circle with radius R=1 .

the limits of integration on z:

you can see in sketch : 0<=z<=U+V (of course just for u & v that in region of the projection )
TNX ...
 
  • #4
Yeah, the ant thing . . . not a good way to start sedaw. Did you just enter "cotant" in latex and it partitioned it that way? Just use [itex]\cot[/itex]. But even worst, that picture looks nothing like what I think your V is. Guess the J is Jacobian. But I wouldn't try to change variables until I first tried to solve it the old-fashioned way: just use x, y, and z. Oh, but I would also try to plot a real-looking picture first. Is the volume that part under the paraboloid [itex]z=x^2+y^2[/tex] contained by the transparent "square-tube" of [itex]x^4+y^4=1[/itex] under the paraboloid in the plot below?

If so, can you see how to arrive at:

[tex]V=8\int_0^{1/2^{1/4}}\int_x^{\sqrt[4]{1-x^4}}\left(x^2+y^2\right) dydx[/tex]

That comes out to about 2.22. Would be nice if you already know the answer to see at least if this is on the right track and I realize that's a tough integral to solve symbolically, but it get's you grounded at least with something concrete to work with and then perhaps you can use that integral to then change variables. Maybe not though. It's just a suggestion.
 

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  • #5
ok.. thank you very much i am appreciate your help.
by the way my picture is V for the uvz axis and not xyz .
 

What is volume and how is it calculated?

Volume is the amount of space that an object or substance occupies. It is calculated by multiplying the length, width, and height of an object or by using the appropriate formula for the shape of the object.

Why is volume important in scientific calculations?

Volume is important in scientific calculations because it helps us understand the physical properties of objects and substances. It is also used to determine the amount of a substance present, which is crucial in experiments and research.

What are the units of measurement for volume?

The most commonly used units of measurement for volume are cubic meters (m³) in the metric system and cubic feet (ft³) in the imperial system. Other units include liters (L), gallons (gal), and cubic centimeters (cm³).

How do I calculate the volume of irregularly shaped objects?

The volume of irregularly shaped objects can be calculated by using the displacement method. This involves placing the object in a known volume of water and measuring the difference in volume before and after the object is submerged.

What are some real-life applications of volume calculation?

Volume calculation is used in various fields, such as engineering, architecture, chemistry, and physics. It is used to design buildings, determine the amount of materials needed for construction, measure the volume of liquids in containers, and calculate the density of objects.

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