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Curated by: DFulks Math (15 videos)
What if we could handle derivatives and integrals involving absolute value without using piecewise functions or breaking things into cases? In this video, we'll discover some surprisingly elegant formulas for working with absolute value in calculus. We'll even use integration by parts (!) to evaluate ∫|x| dx, and we'll see a beautiful explanation for why the integral of 1/x is ln|x| rather than just ln(x). Along the way, we'll explore derivatives, u-substitution, graphs, and an interesting connection to the idea of smoothness in higher mathematics. Sometimes a simple mathematical idea turns out to have unexpected beauty! #Calculus #Mathematics #AbsoluteValue