Solving Double Integrals: Sketch and Evaluate

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SUMMARY

The discussion focuses on solving double integrals, specifically evaluating the integral from 0 to 2 and from x² to 4 of the function e^(y²) dy dx. Participants emphasize the importance of sketching the region of integration to visualize the problem. One user expresses difficulty in starting the problem and suggests changing the order of integration as a potential solution strategy. The conversation highlights the necessity of understanding the bounds of integration for effective evaluation.

PREREQUISITES
  • Understanding of double integrals and their applications
  • Familiarity with integration techniques, including integration by parts
  • Ability to sketch regions of integration in the Cartesian plane
  • Knowledge of changing the order of integration in double integrals
NEXT STEPS
  • Study techniques for sketching regions of integration in double integrals
  • Learn how to change the order of integration in double integrals
  • Practice evaluating double integrals with various bounds and functions
  • Explore advanced integration techniques, including polar coordinates for double integrals
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable calculus and double integrals, as well as educators seeking to enhance their teaching methods in this area.

kieranl
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double integrals!

Homework Statement



sketch the region of integration then evaluate the double integral



Homework Equations



[tex]^{2}_{0}[/tex][tex]\int[/tex][tex]^{4}_{x^2}[/tex][tex]\int[/tex]xey2dydx


3. The Attempt at a Solution

I can't even see how to start this problem. I've tried integration by parts but got no where! can some one please give me a direction?
 
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Try changing the order of integration, though I couldn't read what your bounds were =[.
 

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