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, of course. …

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 " dx d x ". …

May 2, 2015 · Okay this may sound stupid but I need a little help... What do $\Large \frac {d} {dx}$ and $\Large \frac {dy} {dx}$ mean? I need a thorough explanation. Thanks.

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 the integral? …

Apr 8, 2018 · I understand the meaning of $\frac {dy} {dx}$ and $\int f (x)dx$, but outside of that what do $dy, du, dx$ etc.. mean? When I took calc I, derivatives and integrals were given a definition, but …

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 impossible for …

Dec 27, 2013 · Δx Δ x, δx δ x and dx d x are used when talking about slopes and derivatives. But I don't know what the exact difference is between them.

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 ...

May 5, 2022 · The notation $\dfrac {dy} {dx}$ is derived from the tangent-slope interpretation of the derivative, that is to take the ratio of the opposite side with the adjacent side. The discrete product …

Possible Duplicate: Indefinite integral of secant cubed How to integrate $\sec^3 x \, dx$? Can someone please give a method, I tried separating $\sec^3 x$ as $\sec x (\sec^2 x)$ then applying by...