# Reversing the order of integration

• s7b
In summary, the conversation revolves around reversing the order of integration for a given integral and changing the limits of integration. The conversation also mentions drawing a picture to understand the limits of integration.
s7b
Hi,

I want to reverse the order of this integration;

integral(from x=0 to x=3) integral(from y=sqrt(x/3) to y=1) of e^(y^3) dy dx

How do I change the limits of integration?

Didn't I tell you what to do in the other thread though? Pretty sure you can move the threads you start (at least you could on the other boards I've been on) by going to Thread Tools

Well I didn't know.
I also don't get how to draw the pictures.

You are told what horizontal (i.e. x goes from and to i.e. between 0 and 3) and you are told what the vertical goes from (i.e. y goes from and to i.e. sqrt(x/3) to 1)

I get that but don't you have to change the limits of integration when you reverse the order of integration?

Yes, you said you don't know how to draw the picture, I told you what the picture would look like. Did you draw it?

## 1. What does it mean to "reverse the order of integration"?

Reversing the order of integration refers to the process of changing the order in which the limits of integration are evaluated in a double or triple integral. This can be useful in certain cases where it is easier to integrate in a different order.

## 2. When is it necessary to reverse the order of integration?

Reversing the order of integration is necessary when the original order of integration leads to a more difficult or impossible integration process. This can occur when the region of integration is better described by changing the order of integration.

## 3. How do you reverse the order of integration?

To reverse the order of integration, you must first determine the new limits of integration by graphing the region of integration and considering the order of the variables in the integrand. Then, you can swap the order of integration and evaluate the integral as usual.

## 4. What are some common mistakes when reversing the order of integration?

One common mistake when reversing the order of integration is incorrectly determining the new limits of integration. It is important to carefully consider the region of integration and the order of the variables to avoid this error. Another mistake is forgetting to change the integrand to reflect the new order of integration.

## 5. Can you reverse the order of integration in a triple integral?

Yes, the order of integration can be reversed in a triple integral just like in a double integral. However, it is important to carefully consider the new limits of integration and change the integrand accordingly. This process may become more complex in a triple integral, so careful consideration and practice are recommended.

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