Questions about double and triple integrals

In summary, Maurice was having troubles with double and triple integrals. He was having trouble understanding the symmetry thing and also had trouble interpreting the integrals. He was also having trouble with choosing the limits of integration.
  • #1
Maurice7510
55
1
Hey,
I was just going through my vector calc textbook for this year and everything was going well until I reached double and triple integrals. My problem is the whole symmetry thing; when does (forgive me, I can't figure out the symbols) the integral from a to b become twice the integral from 0 to a versus becoming zero?
Other than that, I think I was doing fine, but if you guys wouldn't mind posting some double and triple integral questions for me so I could get some practice that would be great.
Thanks,
Maurice
 
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  • #2
Much the same thing as you saw with single integrals: if f(x) is an even function, then [itex]\int_{-a}^a f(x)dx= 2\int_0^a f(x)dx[/itex] and if f(x) is an odd function, then [itex]\int_{-a}^a f(x)dx= 0[/itex]. More generally, if f(x,y,z) is exactly the same in two regions, then the integral over the two is just twice the integral over one:I+ I= 2I. If f(x,y,z) is the same in two regions, except that one is the negative of the other, they cancel and the integral is 0: I- I= 0.
 
  • #3
That helps but there's a couple things: even fcn is where -f(x) = f(x) and odd fcn is where -f(x) = f(-x)? I just kind of forget, sorry. Also, what always bothered me about this is that, for example, if you have a fcn where it's graph is symmetrical with one region negative but equal to the other, how does the area "cancel out"?
 
  • #4
I think another problem I'm having is interpreting the integrals. For example, there's a problem I'm looking at in the textbook, where it asks us to calculate the triple integral of y^2 of, and this is the hard part for me, the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x+3y+z=6. I have no idea how to choose my limits of integration, i.e. integrate from what to what?

If somebody can explain how to choose these, that would be greatly appreciated.
Thanks again,
Maurice
 

1. What is the difference between a double and triple integral?

A double integral is used to find the volume under a surface in two dimensions, while a triple integral is used to find the volume under a surface in three dimensions.

2. How do you set up a double or triple integral?

To set up a double integral, you need to define the boundaries for both the x and y variables and then integrate the function with respect to both variables. To set up a triple integral, you need to define the boundaries for all three variables (x, y, and z) and then integrate the function with respect to all three variables.

3. What is the purpose of using a double or triple integral?

A double or triple integral is used to find the volume under a surface in two or three dimensions, respectively. It is also used in various applications such as calculating mass, center of mass, and moments of inertia.

4. Can you explain the concept of iterated integrals?

Iterated integrals refer to the process of breaking down a double or triple integral into a series of single integrals by integrating with respect to one variable at a time. This allows for easier calculation and understanding of the overall integral.

5. How do you evaluate a double or triple integral?

To evaluate a double or triple integral, you can use various methods such as the Fubini's Theorem, change of variables, or using polar, cylindrical, or spherical coordinates. The method used will depend on the function and the boundaries of the integral.

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