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What does the dx mean in an integral? [duplicate] The " dx d x " lets people think informally that you're multiplying a height, f(x) f (x), by an "infinitesimal width", dx d x, and then taking an infinite sum
Is There a Difference Between $d^2x$ and $(dx)^2$? Here, (dx)2 (d x) 2 means dx ∧ dx d x ∧ d x, and the fact that it vanishes comes from the fact that the exterior algebra is anti-commutative In other words, formally we have d2x = 0 d 2 x = 0 and (dx)2 = 0 (d x) 2 = 0 but for two different reasons
calculus - Integrating 1 dx. - Mathematics Stack Exchange Strictly speaking ∫ x dx ∫ x d x is not a well defined expression, and could be interpreted in a variety of ways Classically, dx d x is regarded as an infinitesimal, and thus you are essentially dividing by zero
calculus - What is the true, formal meaning and reason for the dx . . . Prior to the 1800s, "dx" was considered an "infinitesimal" - a number so close to zero that, for some things, it can be considered actually zero, but wasn't exactly zero In the 1800s, the failure to formalize infinitesimals (and, in my opinion, the growing rise of materialism) led to the belief that infinitesimals were invalid mathematical