Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060227 09:49:07
u substitutionIs any possible u substitution legal so long as you replace dx with an equivilent form of du? A logarithm is just a misspelled algorithm. #2 20060227 16:06:33
Re: u substitutionI mean it makes sense you could replace x^2 with u as a sort of notation for x^2 but for instance, could you replace any function with any functon so long as you find the du equivilent for dx? (or whatever the original variable of integration was) A logarithm is just a misspelled algorithm. #3 20060227 16:39:20
Re: u substitutionIf you want to sub for cos x like that, then u = e^cos(x), so the domain of u is restricted by the range of e^cos(x). Thus, ln(u) is restricted by cos(x). "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 