Double integral - What are the upper and lower bounds?

In summary, the upper limit is always the larger value and for the limits on y integration, -1 should be placed at the upper limit as it is less negative. Please ensure that images are posted in the correct orientation in the future.
  • #1
gtfitzpatrick
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Homework Statement
What are the upper and lower bounds?
Relevant Equations
see picture
241600

Cant get my head around the order of the upper and lower bounds for this, Is it always the higher take away the lower?
 
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I can't get my head around the problem statement -- please type
 
  • #3
gtfitzpatrick said:
View attachment 241600
Cant get my head around the order of the upper and lower bounds for this, Is it always the higher take away the lower?
The upper limit is always the larger value (i.e., more positive or less negative. For the limits on the y integration, ##-e^x < -1##, so -1 is the less negative value, and you are correct to put it at the upper limit of integration.

Also, in the future, if you post an image, please take care to post it in the correct orientation. A lot of members here don't like to have to crane their heads 90° to be able to read an image.
 

Related to Double integral - What are the upper and lower bounds?

1. What is a double integral?

A double integral is a mathematical concept used to calculate the area under a two-dimensional curve or surface. It is essentially the integration of a function of two variables over a specific region in the xy-plane.

2. What are the upper and lower bounds in a double integral?

The upper and lower bounds in a double integral refer to the limits of integration for each variable. The lower bound is the starting point of integration and the upper bound is the ending point. These bounds help define the region over which the integration is being performed.

3. How do you determine the upper and lower bounds in a double integral?

The upper and lower bounds in a double integral are determined by the boundaries of the region over which the integration is being performed. This can be done by looking at the given function or by graphing the function and visually identifying the boundaries of the region.

4. Can the upper and lower bounds be negative in a double integral?

Yes, the upper and lower bounds in a double integral can be negative. This is because the bounds are determined by the boundaries of the region, which can extend into the negative values of the variables.

5. How do the upper and lower bounds affect the value of a double integral?

The upper and lower bounds can greatly affect the value of a double integral. Changing the bounds can result in a different region being integrated over, which can lead to a different value for the integral. It is important to carefully determine the correct bounds in order to obtain an accurate result.

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