The discussion revolves around evaluating a specific integral, with a hint suggesting that the integral equals zero. Participants are exploring various methods and approaches to prove this assertion.
The discussion is active, with participants providing hints and observations. There is recognition of a key insight regarding the relationship between the two functions involved in the integral, which may lead to a more straightforward proof.
Participants note that the two functions in question are inverses of each other on the interval [0,1], which may influence the evaluation of the integral. There is also a reference to the problem being from a specific textbook, which may impose certain constraints on the methods discussed.
Dick said:You can evaluate the integral in terms of the Euler Beta function. Use two different substitutions for each part and properties of the gamma function to show it's zero.
dirk_mec1 said:The integral is in stewart's book problem plus section I very much doubt that the beta function needs to be invoked...
Cyosis said:In this special case it can be done without the beta function. Note that the two given functions are each others inverses on the interval [0,1].
Cyosis said:In this special case it can be done without the beta function. Note that the two given functions are each others inverses on the interval [0,1].