Problem with setting the region of integration

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In summary, the conversation is about a problem with the solution of some integrals. The speaker is confused about the choice of borders for the integral and questions why c is used as the upper limit instead of b/a. The other person explains that for the given domain, c is indeed greater than b/a and therefore, it can be used as the upper limit. They also mention that the area of integration is a triangle and that c is not actually used in the calculation. The speaker expresses their appreciation for the explanation.
  • #1
Amaelle
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Homework Statement
look at the image below!
Relevant Equations
double integrals
Good day !
I have a problem with the solution of the floowing integrals
Indeed i don't understand why they choose such borders for integral
b/a<c
y<c
doesn't mean that y<b/a !
many thanks in advance!

1614189909864.png
 

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  • #2
Amaelle said:
doesn't mean that y<b/a !
For ##(x,y)\in\Omega##, yes that is correct. That's why they can set the upper limit on the outer integral to ##b/a## rather than ##c##, even though ##c## may be greater than ##b/a##.

The area of integration is a triangle with vertices (0,0), (0, b/a), (b,0).

Given that c>b/a, the value of c is not used in the calculation. I think they just put it in the question to confuse people!
 
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that was an amzing shot! thanks a million!
 

Related to Problem with setting the region of integration

1. What is the "region of integration" in a scientific context?

The "region of integration" refers to the specific area or domain over which a mathematical or scientific function is being analyzed or evaluated. It can also refer to the boundaries or limits within which a particular phenomenon or process is being studied.

2. Why is setting the region of integration important in scientific research?

Setting the region of integration is important because it allows for a more precise and accurate analysis of a particular phenomenon or process. By defining the boundaries or limits of the region, scientists can control for extraneous variables and focus on the specific area of interest.

3. What are some common challenges or problems with setting the region of integration?

One common problem with setting the region of integration is determining the appropriate boundaries or limits. This can be particularly challenging when dealing with complex or multidimensional functions. Additionally, inaccuracies in defining the region can lead to errors in analysis and interpretation of results.

4. How can scientists ensure that the region of integration is accurately set?

To ensure the accuracy of the region of integration, scientists can use various techniques such as numerical methods, computer simulations, or physical experiments. It is also important for scientists to carefully consider the variables and parameters involved in the function and carefully define the boundaries or limits of the region.

5. Can the region of integration change in scientific research?

Yes, the region of integration can change in scientific research. As new data and information are gathered, scientists may need to adjust the boundaries or limits of the region in order to account for new variables or refine their analysis. This is a normal part of the scientific process and allows for a more comprehensive understanding of a phenomenon or process.

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