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What does the dx mean in an integral? [duplicate] 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
Is There a Difference Between $d^2x$ and $ (dx)^2$? 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 $ (dx)^2=0$ but for two different reasons
derivatives - Proof of dy=f’ (x)dx - Mathematics Stack Exchange 0 Well the derivative is given by: $$\lim_ {dx \to 0} \frac {f (x+dx)-f (x)} {dx}=\lim_ {dx\to 0} \frac {dy} {dx}$$ By definition the derivative is the rate of change of y with regard to x That's why RHS stands As you realise $\frac {dy} {dx}$ is not just a notation but it's mathematically how derivative is been defined
What does $dx$ mean? - Mathematics Stack Exchange 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 In more general settings, the three interpretations generalize in different ways, so that the "dx" comes to mean different things
What is $dx$ in integration? - Mathematics Stack Exchange 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 of the Riemann sum of f (x) between a and b as the increment of X approaches zero (and thus the number of rectangles approaches infinity)