Problem sheet double integration

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In summary, the conversation is about solving an integral problem involving the function x^3(x^2+y^2) with limits of x between 2 and -4 and y between 5 and 0. The person initially gets an answer of -17426 2/3, but after plugging the formula into Maple, gets an answer of -5860. They discuss their steps, including expanding the brackets and integrating with respect to y and x. They ultimately agree with Maple's answer and discuss potential errors in their integration process.
  • #1
the_godfather
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Homework Statement



[tex]\int\int x^3(x^2+y^2)[/tex] dy dx limts of x between 2 and -4 and y limits between 5 and 0

Homework Equations





The Attempt at a Solution



i get an answer -17426 2/3 which doesn't seem right

plugged the formula into maple and has given me an answer of -5860.

my first step was to expand the brackets.

to get [tex]\int\int x^5 + x^3y^2[/tex] then integrate with respect to dy. put the limits of y in as 5 and 0.

[tex]\int 5x^5 + (125x^3/3)[/tex]
then integrate with respect to x and again put the limits in.
 
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  • #2
I agree with Maple. I also agree with your x integration. Except I would put a minus sign in front because I integrated with a lower y limit of 5 and an upper y limit of 0. Is that what you meant? You'll have to show more intermediate results to be able to tell what you are doing wrong.
 

1. What is double integration?

Double integration is a mathematical technique used to find the definite integral of a function of two variables over a certain region. It involves integrating a function with respect to one variable, and then integrating the resulting function with respect to the other variable.

2. What is the purpose of double integration?

The purpose of double integration is to find the exact value of a function over a specific region. It is often used in physics, engineering, and other scientific fields to calculate quantities such as area, volume, and mass.

3. How do you solve a problem sheet on double integration?

To solve a problem sheet on double integration, you first need to identify the region of integration and the limits of integration for each variable. Then, you can use the properties of integrals and various integration techniques to evaluate the integrals and find the final solution.

4. What are some common challenges when dealing with double integration?

Some common challenges when dealing with double integration include correctly identifying the region of integration, setting up the limits of integration, and choosing the appropriate integration technique. It can also be challenging to visualize the region of integration and determine the correct order of integration.

5. How can I practice and improve my skills in double integration?

The best way to practice and improve your skills in double integration is to work through various problem sheets and practice exercises. You can also consult textbooks and online resources for additional examples and explanations. It is also helpful to review the properties of integrals and different integration techniques.

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