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, …

I know dy/dx for example means "derivative of y with respect to x," but there's another context that confuses me. You will generally just see a dx term sitting at the end of an integral equation an...

These things should be dimensionally correct, and are not so without the " dx dx ". Sometimes one has a dot-product or a cross-product or a matrix product or some other sort of product …

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.

Jan 12, 2016 · These identities for $\int_0^1 x^ {-x}\ dx$ and $\int_0^1 x^x\ dx$ are sometimes called the "sophomore's dream". Look that up on Wikipedia.

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 …

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 …

Dec 27, 2013 · Well, $\delta x$ means different things depending on the context. For example, it has a particular meaning in variational calculus, and a completely different one in functional …

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 …