1st Moment of Area, Double Integrals

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SUMMARY

The discussion centers on the calculation of the 1st moment of area using double integrals in a statics course. The user, Jacob, expresses confusion over differing methods for solving double integrals as taught by his professor compared to his calculus textbook. Jacob seeks clarification on the correct approach to apply for determining the moment of area, specifically noting that the area in question is homogeneous. The conversation highlights the importance of understanding various integration techniques in statics applications.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with the concept of the 1st moment of area
  • Knowledge of homogeneous materials in engineering
  • Basic principles of statics
NEXT STEPS
  • Review the method for calculating the 1st moment of area using double integrals
  • Study different techniques for solving double integrals in calculus
  • Examine examples of homogeneous area calculations in statics
  • Explore resources on integrating functions over specific regions
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Students in engineering or physics courses, particularly those studying statics and mechanics, as well as educators seeking to clarify integration methods for the 1st moment of area.

simpsoncan2
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Hello I am in a statics course and am having difficulty solving a problem. In this problem I am supposed to find the 1st moment of the area. I have attached some photos of the work I have completed but it differs from the way my professor does these problems.

P9200478.jpg

P9200479.jpg

P9200480.jpg


His method for solving the double integrals is different from the method that I remeber and what my Cal book states as the proper way. Here is an example of how he is doing double integrals for the same problem, these are straight from my inclass notes:

P9200481.jpg


If someone has some insight on which method is correct and what I should do differently to solve my moment of an area problem I would really appreciate some help.

Thanks, Jacob
 
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Oh and the area/plate on the graph is homogeneous.
 

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