I need some practice problems involving double integrals

In summary, the conversation revolved around a request for resources on double integrals in a Probabilistic Models in Biology class. The person asking the question had not studied Calculus IV since fall of 2016 and was looking for free resources with practice problems. Recommendations were made for websites such as mathinsight.org and tutorial.math.lamar.edu, as well as a pdf with practice problems. The person also received encouragement to use any available resources on multivariable, vector, or advanced calculus.
  • #1
Eclair_de_XII
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I'm in my Probabilistic Models in Biology class, and the professor just brought up the subject of double integrals. I haven't done Calculus IV since fall of 2016, so naturally, I kind of forgot how to do integrals with more than one integrand. Can anyone recommend me any (hopefully, free) pdf's or resources that contain such practice problems? Double integrals are being emphasized in this class right now, so if anyone could link me to a resource with problems of this caliber, it would be much appreciated.
 
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  • #2
Eclair_de_XII said:
I'm in my Probabilistic Models in Biology class, and the professor just brought up the subject of double integrals. I haven't done Calculus IV since fall of 2016, so naturally, I kind of forgot how to do integrals with more than one integrand. Can anyone recommend me any (hopefully, free) pdf's or resources that contain such practice problems? Double integrals are being emphasized in this class right now, so if anyone could link me to a resource with problems of this caliber, it would be much appreciated.

You can take a look at https://mathinsight.org/thread/multivar for explanation and http://tutorial.math.lamar.edu/Problems/CalcIII/DIGeneralRegion.aspx and https://faculty.math.illinois.edu/~hildebr/461/doubleintegrals-sol.pdf for practice problems, and every multivariable/vector/advanced calculus can do the work.
Good luck.
 
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1. What are double integrals?

Double integrals are mathematical tools used to calculate the volume under a surface in a 3-dimensional space. They involve integrating a function with two variables over a specific region in the x-y plane.

2. Why do I need to practice double integrals?

Practicing double integrals can help improve your understanding and skills in solving 3-dimensional problems. It also helps in visualizing and manipulating complex functions in multiple variables, which is essential in many fields of science and engineering.

3. How do I set up a double integral?

To set up a double integral, you need to determine the limits of integration for both variables, which are usually the bounds of the region in the x-y plane. Then, you need to write the integrand in terms of the two variables and specify the order of integration (either dx dy or dy dx).

4. What are some common applications of double integrals?

Double integrals have many applications in mathematics and science, including calculating volumes, finding the center of mass of an object, determining probabilities in statistics, and solving problems in electromagnetism and fluid mechanics.

5. How can I improve my skills in solving double integral problems?

The best way to improve your skills in solving double integral problems is through practice. Start with simple problems and gradually move on to more complex ones. You can also seek help from textbooks, online resources, or a tutor if needed.

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