1, different mathematical expressions:

Differential: There are some differences in writing between derivative and differential. For example, y'=f(x) is derivative and dy=f(x)dx is differential.

Integral: Let f(x) be the original function of function F(x). We call all primitive functions f(x)+c (c is an arbitrary constant) indefinite integrals of function f(x). The mathematical expression is: if f'(x)=g(x), there is ∫ g.

2. Different geometric meanings:

Differential: let Δ x be the increment of point m on the curve on the abscissa y = f(x), Δ y be the increment of the curve on point m corresponding to Δ x on the ordinate, and dy be the increment of the tangent of the curve on point m corresponding to Δ x on the ordinate. When | Δ x | is very small, |Δy-dy | is much smaller than |δx | (high-order infinitesimal), so we can use a tangent line segment to approximate the curve segment near point M.

Integral: The motive force of integral development comes from the demand in practical application. In practice, some unknowns can sometimes be roughly estimated, but with the development of science and technology, it is often necessary to know the exact values. If the area or volume of simple geometry is needed, the known formula can be applied. For example, the volume of a rectangular swimming pool can be calculated by length x width x height.

Extended data:

Generally speaking, differential and integral are a kind of function transformation-from a known function to a new function through some internal process, and it is a kind of mapping (correspondence) in which "domain" and "range" are function sets.

If the difference is not considered as a constant, then differentiation and integration are inverse transformations: first, differentiate a function, and then integrate it, which is equal to itself; Integrate and then differentiate a function equal to itself.

References:

Baidu Encyclopedia-Difference

Baidu encyclopedia-integral