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. …

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 …

May 2, 2015 · dy dx = lim h→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 in this case. …

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 calculus...

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.

Mar 5, 2011 · In Leibniz notation, the 2nd derivative is written as $$\dfrac {\mathrm d^2y} {\mathrm dx^2}\ ?$$ Why is the location of the $2$ in different places in the $\mathrm dy/\mathrm dx$ terms?

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 realize …

The indefinite integral is introduced in the notation ∫f(x)dx ∫ f (x) d x without explaining the meaning of dx. At first I thought it was mere notation to indicate what variable we are integrating in reference to. But …