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...

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 …

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.

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 · I'm taking differential equations right now, and the lack of fundamental knowledge in calculus is kicking my butt. In class, my professor has done several implicit differentiations. I …

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 …

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 …

The dx in the integral is a representation of the fact that the integral is obtained as an area, so multiplying the "average" of the function value at each point by an infinitesimal interval.

I just finished taking my first year of calculus in college and I passed with an A. I don't think, however, that I ever really understood the entire $\\frac{dy}{dx}$ notation (so I just focused on ...