Rule of thumb for double integral order

In summary, the rule of thumb for double integral order is to integrate the innermost function first, then the outermost function, and to remember to use the appropriate limits of integration for each variable. This method is known as the "inside-out" approach and can be applied to both rectangular and polar coordinates. It is important to pay attention to the order of integration to ensure accurate evaluation of the integral. Additionally, if the limits of integration are in terms of a specific variable, it is necessary to substitute that variable in both the inner and outer integrals.
  • #1
mrcleanhands
Is there any rule of thumb for which variable should be integrated first?, i.e. to make the whole process of double integration easier.
 
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  • #2
That is the rule of thumb - do it in the order that makes the integration easiest.
What counts as "easy" is too variable to get more specific.
 

Related to Rule of thumb for double integral order

1. What is the rule of thumb for determining the order of a double integral?

The rule of thumb for determining the order of a double integral is to count the number of variables in the integrand. This will give you the order of the integral, which corresponds to the number of nested integrals needed to evaluate it.

2. How does the order of a double integral affect the evaluation process?

The order of a double integral determines the number of nested integrals needed to evaluate it. The higher the order, the more complex the evaluation process becomes.

3. Can the order of a double integral change during the evaluation process?

No, the order of a double integral is determined by the number of variables in the integrand and cannot change during the evaluation process.

4. How can I simplify a double integral with a high order?

If you encounter a double integral with a high order, you can often simplify it by using properties of integration, such as symmetry or change of variables. It may also be helpful to break the integral into smaller parts and evaluate them separately.

5. Are there any situations where the rule of thumb may not apply?

Yes, there are some integrals with special properties that may not follow the rule of thumb for determining the order. These cases often require a different approach to evaluate the integral.

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