Question about a double integral.

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SUMMARY

The discussion revolves around solving the double integral of the function xcos(y) bounded by the curves y=0, y=x^2, and x=1. The user initially faced confusion when substituting x^2 into the integral but resolved the issue by adjusting the limits of integration from 0 to 1. This adjustment led to a successful solution of the integral, demonstrating the importance of correctly setting integration bounds in double integrals.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with the concept of integration bounds
  • Knowledge of the function xcos(y)
  • Basic skills in sketching curves and regions for integration
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  • Study the method of changing integration limits in double integrals
  • Learn about the application of double integrals in calculating areas and volumes
  • Explore the use of polar coordinates in double integrals
  • Review examples of integrating functions over complex regions
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Students and educators in calculus, mathematicians working with integrals, and anyone looking to deepen their understanding of double integrals and their applications.

DavidAp
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The double integral xcosy is bounded by y=0, y=x^2, and x=1. I was able to integrate almost wholly through; however, toward the end I was unsure what to do when i was asked to plug in x^2 into x^2. What do I do?!

Here is an image of my work on the white board. Please, if my hand writing is illegible tell me and I would be more than happy to type it all out for you.
Thank you for taking the time to review my question.

2vjajrn.jpg
 
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Here you go, you can remove that giant image via edit.
2vjajrn.jpg
 
Thank You!

I solved it after a triple glance at the board! I knew something had to be wrong so I change my first integral to be 0 -> 1 and it worked! I'm just putting this out there because I don't know how to delete a thread, but thank you anyways forum!
 
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