Solving Integration by Parts with a Reduction Formula

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SUMMARY

The discussion focuses on using integration by parts to prove a reduction formula, specifically addressing the confusion regarding the form of the integral involving a power of n rather than a square root. Participants clarify that in the integration by parts method, 'a' is a constant, 'x' is the variable, and 'n' must also be a constant. The conversation emphasizes the importance of correctly identifying 'u' and 'dv' in the integration by parts formula to proceed with the proof.

PREREQUISITES
  • Understanding of integration by parts
  • Familiarity with reduction formulas in calculus
  • Knowledge of constants and variables in mathematical expressions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review the integration by parts formula and its applications
  • Study reduction formulas in calculus for various functions
  • Practice problems involving integration by parts with different powers
  • Explore the relationship between constants and variables in integrals
USEFUL FOR

Students studying calculus, particularly those learning about integration techniques and reduction formulas, as well as educators looking for examples to illustrate integration by parts.

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Homework Statement



Use integration by parts to prove the reduction formula:
http://img214.imageshack.us/img214/1234/24206074.jpg


Homework Equations





The Attempt at a Solution


what confuses me about this question is that its not in the form sqrt(a2 + x2) but its in ^n instead of sqrt.. so how do i do that?
 
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Can you elaborate more on why that confuses you? It seems a is a constant and x is the variable to start off. n also has to be a constant. Just do integration by parts, just like you pointed out in the title. Do you remember how to do integration by parts? I'll start you off, dx will be dv in the Integration by parts equation and the rest will be u.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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