How Does Integration by Factors Relate to the Product Rule and FTC?

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The discussion centers on the relationship between integration by factors, the product rule, and the Fundamental Theorem of Calculus (FTC). A user struggles with proving an integral equality involving a differentiable function over the interval [0, 2π], leading to confusion and attempts to apply integration by factors. Participants suggest testing specific functions like f(x) = cos^2(x) and using trigonometric identities to simplify the integrals. Ultimately, it is concluded that integration by factors is not necessary, as the problem can be solved using known trigonometric identities and the FTC, highlighting the connection between integration by parts and the product rule. The conversation emphasizes the importance of recognizing these relationships in solving integral problems.
  • #31
PeroK said:
Note that as long as you remember the product rule, you can forget integration by parts entirely.
Exactly! IBF is actually product rule +FTC.
 

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