What is differentiation and integration?

Question

Can someone explain what is the "practial" meaning of differentiation and integration? please explain with examples. may be with some examples in physics would be better.

Answer 1

Differentiating is really just finding the slope of a curve at any given point. Since virtually anything that happens can be graphed as a curve, the slope gives you a rate or a rate of change depending on graph is defined.



For example if you graph your position vs time. The slope of the curve is the speed that you are going.



If you graph the speed vs time, then the slope is the acceleration.



One is a rate the other is a rate of change.



Integration is just finding the area under a curve. Again, virtually all activities ca be graphed. The areas under the curves help to solve a myriad of problems.



Look at the speed vs time graph from above. The area under the curve is the distance that you traveled. So that you can go from rates of change to rates and from rates to total quantities.



Hope this helps.

Answer 2

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 3

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 4

What Is Differentiation

Answer 5

A simple meaning:-

Differentiation means distruction.

For eg:diff(x^3+2x^2+3x+7)

=3x^2+4x+3 (diff x^n=nx^n-1)



& Integration means construction.

For eg:int(x^3+2x^2+3x+7)dx

=x^4/4+2x^3/3+3x^2/2+7x (int x^n=x^n+1/n+1)

Answer 6

Practically speaking, the derivative of a function can be thought of as the slope of a line tangent to the function.



The integral of a function may be thought of as the 'area' under the curve of the function.





Doug

Answer 7

Yet two more inabilities of our President.



He can't differentiate between the simplest, most clearly different groups or objects (his *** from a hole in the ground; Arabs from Muslims; a participle from a predicate).



He can't integrate his life experience (his struggle with drug and alcohol abuse as a young man) with his extraordinarly lacking compassion.