Quick question on double/triple integrals for area and volume

In summary, the conversation discussed how to correctly format formulas on a forum and the importance of attaching images with appropriate sizes. The formula for the integral of 0 was also provided.
  • #1
Lifprasir
16
0
I do not know how to formulate formulas on this forum so I just wrote it neatly on a piece of paper and linked it.

http://puu.sh/8fwXr.jpg [Broken]

Thankss.
 
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  • #2
Would you edit your post to attach a new image that is smaller? The maximum width should be about 900 pixels. Yours is about 1200 pixels, so doesn't fit in the window.

To answer your question. If f(x, y) = 0, then the integral will be zero.

##\int \int 0 dA = \int \int 0 r dr d\theta = 0##

If the integrand is identically zero for any kind of integral, then the value of the integral is zero.
 

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

A double integral is used to find the area under a surface in two-dimensional space, while a triple integral is used to find the volume under a surface in three-dimensional space.

2. How do I set up a double integral for finding area?

To set up a double integral for finding area, you need to first determine the limits of integration for both the x and y variables. Then, you need to integrate the function over the defined limits using the appropriate integration method (e.g. rectangular, polar, etc.).

3. Can I use a double integral to find the volume of a solid?

No, a double integral can only be used to find the area under a surface in two-dimensional space. To find the volume of a solid in three-dimensional space, you will need to use a triple integral.

4. How can I use a triple integral to find the volume of a solid?

To use a triple integral to find the volume of a solid, you need to determine the limits of integration for all three variables (x, y, and z). Then, you can integrate the function over these defined limits using the appropriate integration method (e.g. rectangular, cylindrical, spherical, etc.).

5. Is there a specific order in which I should integrate the variables in a triple integral?

Yes, the order of integration in a triple integral does matter. The general rule is to integrate the variables from the innermost to the outermost, starting with the variable that has the smallest range of integration. However, in some cases, it may be more convenient to integrate in a different order based on the shape of the region and the function being integrated.

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