2.6.62 inverse integrals with substitution

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SUMMARY

The discussion centers on the application of substitution in inverse integrals, specifically referencing problem 2.6.62 from an Overleaf document. Participants confirm the correctness of the substitution process but highlight a critical error where the differential was incorrectly stated as $du=dx$ instead of the correct $\dfrac{du}{4} = dx$. This emphasizes the importance of precise notation in calculus, particularly when dealing with integrals and substitutions.

PREREQUISITES
  • Understanding of calculus concepts, particularly integration and substitution methods.
  • Familiarity with LaTeX for typesetting mathematical expressions.
  • Knowledge of Overleaf as a collaborative writing tool for LaTeX documents.
  • Basic proficiency in differential notation and its application in calculus.
NEXT STEPS
  • Review the principles of substitution in integrals, focusing on common pitfalls.
  • Explore advanced LaTeX techniques for creating custom macros in Overleaf.
  • Study the implications of differential notation in calculus to avoid common errors.
  • Practice solving similar inverse integral problems to reinforce understanding of substitution.
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Students and educators in mathematics, particularly those studying calculus and integral techniques, as well as anyone using Overleaf for mathematical documentation.

karush
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View attachment 9266
ok this is from my overleaf doc
so too many custorm macros to just paste in code
but I think its ok,,, not sure about all details.
appreciate comments...

I got ? somewhat on b and x and u being used in the right places
 

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karush said:
ok this is from my overleaf doc
so too many custorm macros to just paste in code
but I think its ok,,, not sure about all details.
appreciate comments...

I got ? somewhat on b and x and u being used in the right places
Ummm...

What exactly is your question?

-Dan
 
OK this one was kinda obvious but usually that is where I make the errors especially where there is substitution.
I post another one here soon.:cool:
 
karush said:
View attachment 9267
That all looks correct to me, except that at one point in the solution of 6.6.62 you have written $du=dx$. That should be $\dfrac{du}4 = dx$ (which is what you have correctly used in the following line).
 

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