Iterated Integrals - (just writing one for a region)

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SUMMARY

The discussion focuses on calculating double integrals over a bounded region R in the xy-plane, defined by the curves y=x² and y=x+2. Participants explored how to express the double integral of a function f(x,y) over region R as iterated integrals, specifically using the formats dx dy and dy dx. The application of Fubini's Theorem is central to this process, allowing the transformation of the double integral into iterated integrals. The conversation concludes with a successful resolution of the problem after collaborative assistance.

PREREQUISITES
  • Understanding of double integrals in multivariable calculus
  • Familiarity with Fubini's Theorem
  • Ability to sketch and analyze bounded regions in the xy-plane
  • Knowledge of iterated integrals and their notation
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  • Study the application of Fubini's Theorem in various contexts
  • Practice converting double integrals to iterated integrals with different functions
  • Explore graphical methods for visualizing bounded regions in the xy-plane
  • Learn about the implications of changing the order of integration in double integrals
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Students and educators in calculus, particularly those focusing on multivariable calculus and integration techniques, as well as anyone seeking to deepen their understanding of iterated integrals and Fubini's Theorem.

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R is a bounded region in xy plane defined by y=x2 and y=x+2
a) if f(x,y) is a func. defined in region R, describe how to write double-integralR[f(x,y)dA] as a sum of one or more iterated dx dy integrals.
b) if f(x,y) is a func. defined in region R, describe how to write double-integralR[f(x,y)dA] as a sum of one or more iterated dy dx integrals.


2. Homework Equations
Fubini's Theorem



3. The Attempt at a Solution
I sketched the graph and I would assume you would subtract the two graphs for dy dx.. but either way, I'm not sure what exactly to do. Any help will be appreciated, thanks.
 
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