A "signed definite integral" for computing work and other "net change" calculations. The value of an expression such as $\int_0^1 x^2\,dx$ comes out the same under all these interpretations, …

If f(x) f (x) is in meters per second and dx d x is in seconds, then f(x)dx f (x) d x is in meters, and so is the integral. These things should be dimensionally correct, and are not so without the " …

May 2, 2015 · dy dx =limh→0 f(x + h) − f(x) h. d y d x = lim h → 0 f (x + h) f (x) h and this is is (again) called the derivative of y y or the derivative of f f. Note that it again is a function of x x …

I am working on trying to solve this problem: Prove: $\\int \\sin^n{x} \\ dx = -\\frac{1}{n} \\cos{x} \\cdot \\sin^{n - 1}{x} + \\frac{n - 1}{n} \\int \\sin^{n - 2}{x ...

These identities for dx d x and dx d x are sometimes called the "sophomore's dream". Look that up on Wikipedia. May 9, 2012 at 8:04 How do you know it's legal to switch the summation and …

Apr 8, 2018 · I understand the meaning of dy dx d y d x and ∫ f(x)dx ∫ f (x) d x, but outside of that what do dy, du, dx d y, d u, d x etc.. mean? When I took calc I, derivatives and integrals were …

Here, $ (dx)^2$ means $dx \wedge dx$, and the fact that it vanishes comes from the fact that the exterior algebra is anti-commutative. In other words, formally we have $d^2x=0$ and $ …

Jan 9, 2015 · 8 dx d x is really an enigma in calculus and differential equations. Leibniz treated it as an “infinitesimal”—a number smaller than any positive number but larger than 0 0. In …

Here, δn =xn −xn−1 δ n = x n x n 1 is providing some measure of how important the bit of space between xn−1,xn x n 1, x n is in computing the integral. The dx d x is what keeps track of that …

Sep 9, 2020 · But then others told me that "dx" is part of what's being integrated, and they started saying that we're led to believe that its just a delimiter in early courses because it'd be …