0

Guest

Courses New

how to integrate greatest integer function

how to integrate greatest integer function

Grade:

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
integration of [x].dx (greatest integer function) , limits from 0 to 1.5
[x] =
{ 0 .... 0 = x < 1
{ 1 .... 1 = x < 2

we have several discontinuous parts here... we actually have an improper integral...

integral of [x] dx from 0 to 1.5
= integral of [x] dx from 0 to 1 + integral of [x] dx from 1 to 1.5

= integral of 0 dx from 0 to 1 + integral of 1 dx from 1 to 1.5

= 0.5

like this example in every question we break the limit in to parts like 0 to 1 ,1 to 2 ,2to 3 and so on.
[x]={0, 0=<x<1
{1, 1=<x<2
{2, 2=<x<3
...............
...............
and in ths way we break the integral into parts and we integrate separate integral .

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

Think You Can Provide A Better Answer ?

Other Related Questions on Integral Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More