Integration & Derivatives ,Newtons

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Main Question or Discussion Point

Please can anyone help me to understand what exactly Integration & derivatives are.
Please dont tell in form of limits & continuity. But tell in details of , what we exactly do when we use these functions. Please explain with a practicle example.
I will appreciate your efforts.

thanking You!

Answers and Replies

  • #2
Derivative is nothing but the rate of change of one variable with respect to the other. Not all changes are derivatives but the infinitesmal small changes. For example the concept of derivatives can be understood by simple example. Suppose you have a plant, and it grows 0.5 meter in one year(360) days. and in one month it grows ofcourse 0.5/12(where twelve number is months in 1 year), now the next question is how much it grows in one day? answer=0.5/(12*30). the next question is how much it grows in one second Answer=0.5/(12*30*24*60*60). The next question is how much it grows in 100th of second Answer=0.5/(12*30*24*60*60*100). similarly for 1000000th of second can be calculated. This is what derivative tells an infinitesmal change ie growth with respect to time. here independent variable is time and dependent is growth. so what we are doing just calculating the infinitesmal change in length(growth) with respect to the time. If you reverse the phenomenon, that will be integration simple. ie in 1month ? answer=0.5/(12). what about in a year. that will be with the help of integrations. Answer=0.5.
Similarly see the displacement. the rate of change of displacement with respect to time is velocity. it means for very small change in length with respect to small change in time provided limit exist. limit is nothing but only means the infinitesmal approch. because we cannot go, ie its tedious to say what would be growth of plant for 1000000000000000000th of second but limit makes it easy ie limit time change approaches 0.
If you reverse the velocity ie integration you get displacement. similarly the acceleration is time rate of change of velocity with respect with time. and reverse ie antiderivative or integration will result velocity. Note: if you don't provide limit this will not be exact derivative it will be approximate derivative. hope answer is quite clear. but if not you can ask further.