How to Apply Leibnitz Rule When Integration Limits Depend on a Variable?

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SUMMARY

The discussion focuses on applying Leibnitz's Rule for differentiation when the integration limits are functions of the variable of differentiation. The specific function under consideration is F(a,x) = ∫[c to c+h(a)] f[g(a,x)] dx. Participants clarify that traditional applications of Leibnitz's Rule typically assume constant limits, but the case where limits depend on a variable requires additional considerations. The discussion highlights the need for further resources to fully understand this advanced application of Leibnitz's Rule.

PREREQUISITES
  • Understanding of Leibnitz's Rule for differentiation
  • Familiarity with definite integrals and their properties
  • Knowledge of functions and their derivatives
  • Basic calculus concepts, including limits and continuity
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  • Research advanced applications of Leibnitz's Rule in calculus
  • Study the implications of variable limits in integration
  • Explore resources on differentiating under the integral sign
  • Examine case studies or examples involving F(a,x) with variable limits
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Students, educators, and professionals in mathematics, particularly those studying calculus and advanced integration techniques.

Economist2008
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Does anybody know, how to find the derivative of the F with respect to a? As far as I know the Leibnitz rule is only applicable, when the integration limits do not depend a. But what happens, when one of the limits is a function of a?

F(a,x)=\int ^{c+h(a)}_{c} f[g(a,x)] dx

Thank you so much!
 
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Ups, the books I looked at didn't cover this case.
Thank you very much!
 

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