Oct 7, 2015 · dx (t)/dx vs. dx/dx Ask Question Asked 10 years, 4 months ago Modified 10 years, 4 months ago

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. …

Jan 4, 2026 · At this point, the new integral is of a similar form to the original, and the process does not seem to terminate. From here I am stuck. Question: Does the integral $$ \int e^ {x^2}\sin x\,dx $$ …

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.

Sep 9, 2020 · 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 …

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...

The symbol used for integration, $\int$, is in fact just a stylized "S" for "sum"; The classical definition of the definite integral is $\int_a^b f (x) dx = \lim_ {\Delta x \to 0} \sum_ {x=a}^ {b} f (x)\Delta x$; the limit …

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.

Nov 27, 2025 · The notation $\int_a^b f (x) \, dx$ is a reminder of what happens in a Riemann sum. People get carried away and start abusing the notation sometimes.

What if we want to look at the change of the change? Well, notationally we write d2y dx2 = d dx(dy dx) d 2 y d x 2 = d d x (d y d x) In the previous notation, this would be f′′(x) f ″ (x) and we just 'assume' we …