Calculating Volume using triple integrals

  • Thread starter amooo
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  • #1
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Homework Statement



please help me in determining the volume of the solid bounded by

y^2 = 4x
x^2 = 4y
y = 3
x + y =3
z = x - y

i need to use triple integrals

Homework Equations



v = v1 + V2 + V3

The Attempt at a Solution



V1 = triple integral of dz dy dx
 

Answers and Replies

  • #2
HallsofIvy
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"v= v1+ V3+ V3" makes no sense if you don't tell us what V2 and V3 are!
Have you done anything at all on this? To start with have you graphed the first 4 equations?
 
  • #3
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yes i have plotted the graph. and have determind the limits to be used

i have also calculated the triple integral for dz dy dx,
V1 = triple integral of dz dy dx

now i have to calculate V2 =triple integral of dy dz dx
and V3 = triple integral of dx dz dy

i want to know whether i have to change the limits of these integrals or i should continue with the limits i used for calculating V1

I m new to this so plz guide
 
  • #4
35,238
7,058
V1 will give you the volume of the region, and so will V2 and V3. You don't need to add them together, and it should be the case that V1 = V2 = V3.

Inasmuch as each integral uses a different order of integration, your limits of integration are going to be different for each iterated integral.

Does the problem ask you to calculate all three of these iterated integrals? If not, the only purpose in doing this is as a check on your work.
 
  • #5
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Thanks Mark for the input

How do i calculate limits for V2 and V3.... any hint for this

al;so if u can refer me some tutorial ...id be grateful .

m able to solve the probs....but the idea is still not that clear to me

Thanks
 
  • #6
35,238
7,058
How did you find the limits of integration for your first integral? What did you get for these limits of integration?
 
  • #7
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a friend of mine helped a bit.....but i m not sure for the next 2

also i dont know how to get limits from graph.

my limits for first attempt are

0 - (x-y) for z
(3-x) - (2 sqrt x ) for y
1 - 2 for x
 
  • #8
35,238
7,058
Are you sure that this is all of the given information on the solid region?
y^2 = 4x
x^2 = 4y
y = 3
x + y =3
z = x - y

You have four "cylinders" that act as vertical walls, and you have one plane, z = x - y, that is either the top or bottom. It seems to me you need one more plane to bound the other end.

I haven't worked this out, but the limits you showed for the integral in the order dz dy dx doesn't seem to match the region, and so shouldn't produce the correct value.
 

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