Solving Double Integrals Using U-Substitution

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    Calc 3 Integration
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SUMMARY

The discussion focuses on solving double integrals using U-substitution, specifically with the substitution U = xy² and du = 2xy. The user initially struggled to determine whether to apply integration by parts or substitution but ultimately resolved the problem using U-substitution. The constant x was factored out during the process, simplifying the integration significantly. This method is confirmed as effective for tackling similar double integral problems.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with U-substitution technique
  • Knowledge of integration by parts
  • Basic algebraic manipulation skills
NEXT STEPS
  • Practice solving double integrals using U-substitution
  • Explore advanced techniques in integration by parts
  • Review examples of U-substitution in multiple dimensions
  • Learn about Jacobians in the context of changing variables in integrals
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Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to enhance their teaching methods for double integrals.

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Homework Statement



Attached below

Homework Equations





The Attempt at a Solution




So I cannot figure this out. Would this be integration by parts? or by substitution.. It provides me with an answer but no reasoning behind it and I cannot figure it out =/
 

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xtrubambinoxpr said:

Homework Statement



Attached below

Homework Equations





The Attempt at a Solution




So I cannot figure this out. Would this be integration by parts? or by substitution.. It provides me with an answer but no reasoning behind it and I cannot figure it out =/

PF rules require you to show your work. What have you tried so far?
 
Ray Vickson said:
PF rules require you to show your work. What have you tried so far?

I had done so much work I didnt want to type it and was going to upload a picture, But indeed I figured it out.. Using U sub with U = xy^2 du = 2xy and x was a constant so it was factored out leaving everything peachy!
 
xtrubambinoxpr said:
I had done so much work I didnt want to type it and was going to upload a picture, But indeed I figured it out..
You don't have to show us all your work - just give us some indication that you have done something.
xtrubambinoxpr said:
Using U sub with U = xy^2 du = 2xy and x was a constant so it was factored out leaving everything peachy!
 

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