Differentiation and integration?

Question

I got told that they were opposites like addition and subtraction or multiplication and division.

Can some one explain this to me using a basic ‘Differentiation is, opposed to integration which is’ sort of explanation.

Thankx

Answer 1

Differentiation is like splicing a function into all it's instantaneous changes. Integration is then the process of putting all the pieces back together. In other words, integration is adding up all the instantaneous changes to get the function back.



The word "differentiation" could refer to differentiating from point to point. In other words, identifying the instantaneous change from one point to the next. It could also refer to breaking a function up into its "different" instantaneous changes.



"Integration" refers to the process of "integrating" a lot of the instantaneous changes back into one whole. This "whole" is the same entity that got broken up (differentiated) in the first place. So integration is the reverse of differentiation.

Answer 2

Integrating a given function results in a function whose derivative is the given function. That's why Integration is used in the calculation of things as the areas and volumes of irregular shapes and solids



Whearas Differentiation is the mathematical process of obtaining the derivative of a function.



Hope this will explain your question.

Answer 3

The selection of optimum values for time constants by using appropriate graphs is discussed. The action of the differentiating and integrating time constants is to reduce the frequency response of the amplifier at the low- and high-frequency ends, respectively. Because of the nature of the pulse fed to the amplifier, its duration may be shortened by reducing the differentiating time constant, thereby increasing the resolving power. In addition, the signal-tonoise ratio, and also the resolving power, may be maximized by having the two time constants equal. Points to be considered when choosing the time constants are summarized. An example of the method employed in choosing the most suitable value of T/sub 1/ and T/sub 2/ in a specific case is given. (P.C.H.)

Answer 4

differentiating implies reducing an expression by an order each time. integrating raises the degree of the polynomial. differentiantion finds a slope, or only a line whereas integration gets the whole surface area or volume