How to carry units in integration

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SUMMARY

The discussion focuses on the integration of the function -4x^2/2 + 4x over the interval from 0 to 10 feet to solve for deflection, with forces measured in kips. The user expresses confusion regarding the resulting units, which the textbook states as k-ft³. It is established that when integrating, the resulting units correspond to the product of the units on the axes, leading to the conclusion that the correct unit for deflection in this context should be kip-ft, not k-ft³.

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  • Understanding of calculus, specifically integration techniques.
  • Familiarity with units of measurement in structural engineering, particularly kips and feet.
  • Knowledge of deflection concepts in mechanics.
  • Basic grasp of dimensional analysis to verify unit consistency.
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  • Explore the implications of unit conversions in engineering problems, particularly in mechanics.
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Students in engineering disciplines, particularly those studying mechanics and structural analysis, as well as professionals involved in calculating deflection and understanding unit conversions in engineering contexts.

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Homework Statement


I am trying to integrate from 0 to 10 ft -4x^2/2+4x. I am solving for deflection. The forces are in kips. Somehow the book ends up with k-ft^3. I don't understand how I would carry units in an integration. Any help please?


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The Attempt at a Solution

 
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Normally integrating gives an area which would give the product of the units on the axes. I'd be inclined to think you'd get kip-ft. Are you sure the units are correct?
 

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