# When you transform a double integral that goes over a set

• vacuum
In summary, the speaker is asking if there is a specific method or formula for changing the limits of integration in a double integral that goes over a set D < RxR bounded on the y-axis by g1(x) and g2(x). They also mention that there is no general formula for this and it can be more complicated depending on the specific region. They thank the person for their response.
vacuum
Here's the deal:

When you transform a double intergral that goes over a set
D < RxR bounded on y-axes by g1(x) and g2(x) in two "normal" ones(litteral translation from my language would be subsequent integrals - don't know the word in English) how do you swap the integrals by x and by y(taking y from y1=const to y2=const and x from h1(y) to h2(y)) without visualising the surface itself?

In other words is there any recipe for this kind of transformation or is it always done ad hoc i. e. drawing a picture which you try to figure out?

The English phrase is "repeated integral" or "iterated integral".

There is no general formula for changing the limits of integration.

Depending on the specific regions, the integral can be MUCH more complicated one way than the other.

Thanks!

## 1. What is the process for transforming a double integral?

The process for transforming a double integral involves changing the variables and limits of integration in order to express the integral in a different coordinate system. This is typically done to simplify the integral or make it easier to solve.

## 2. What is the purpose of transforming a double integral?

The purpose of transforming a double integral is to make it easier to solve by changing the coordinate system or simplifying the integrand. This can also help to reveal patterns or symmetries in the integral that may not have been apparent in its original form.

## 3. What are some common coordinate systems used for transforming double integrals?

Some common coordinate systems used for transforming double integrals include polar coordinates, cylindrical coordinates, and spherical coordinates. These coordinate systems are often used for integrals involving circular or spherical shapes, as they can simplify the integrand and limits of integration.

## 4. How do you determine the new limits of integration when transforming a double integral?

The new limits of integration are determined by converting the original limits from the old coordinate system to the new coordinate system. This is typically done by using equations or geometric relationships that relate the two coordinate systems.

## 5. Can any double integral be transformed?

Yes, any double integral can be transformed. However, not all transformations will result in a simpler integral or make it easier to solve. It is important to carefully choose the appropriate transformation based on the integrand and the desired outcome.

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