sir,
i`m finding difficulty in integration of greatest integer function.please give me a brief method of this.
u can break the integration limit from one number to other i mean to say if u hav to integrate [x] (this mean greatest integer function)from 0 to 5 than break intergration into 5 parts i.e. 0 to 1;1 to 2;2 to 3; 3 to 4 ; 4to 5 and than put the values of [x] i.e. between 0 to 1 its value will be 0 ;between 1 to 2 its value will be 1 and so on
THANK YOU
the greatest integer function (gif) means u take only the part that is to the left of the decimal only that is u take only the whole nos for eg 1.234 "has gif equal to 1
This post was originally posted by Gaurav Kukreja .
Hi, First of all you need to get clear with gif. Just see the grapf of a gif. you can see theat it is like a stair. The value of gif changes with evry integral value of the arguement.
To integrate a gif what you need to do is to break the function into limits within which the gif has a fixed value. Suppose you are said to integrate [x^2] from 0 to 1.5.
Take [x^2]=0. therefore x^2 belongs to [0,1), and x belongs to [0,1).
so take the first limit of x as [0,1)
Next take [x^2]=1. Therefore x^2 belongs to [1,2). therefore x belongs to [1,1.414). so take the next limit of x to be [1,1.414).
simillarly take [x^2]=2. i.e. x^2belongs to [2,3). therefore x belongs to [1.414,1.732). but we need to consider only upto 1.5. therefore thake the limit of x to be [1.414,1.5) where []=2.
Integrate within each limit separately and add up.
Gaurav Kukreja