The value of int(0)^(1000) e^(x - [x]) d...

The value of `int_(0)^(1000) e^(x - [x]) dx` (where [.] is the greatest integer function) equals

A

`(e^(1000) - 1)/(1000)`

B

`(e^(1000) - 1)/(e - 1)`

C

`1000 (e - 1)`

D

`(e - 1)/(1000)`

Verified by Experts

Similar Questions

Explore conceptually related problems

The value of int_(0)^(2)[x+[x+[x]]] dx (where, [.] denotes the greatest integer function )is equal to

The value of int_(1)^(10pi)([sec^(-1)x]) dx (where ,[.] denotes the greatest integer function ) is equal to

the value of int_(0)^([x]) dx (where , [.] denotes the greatest integer function)

The value of int_(0)^(2)[x^(2)-x+1] dx (where , [.] denotes the greatest integer function ) is equal to

The value of int_(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greatest integer function of x) is equal to

The value of int_(0)^(10pi)[tan^(-1)x]dx (where, [.] denotes the greatest integer functionof x) is equal to

The value of int_(-1)^(3){|x-2|+[x]} dx , where [.] denotes the greatest integer function, is equal to

The value of lim_(xto0)(sin[x])/([x]) (where [.] denotes the greatest integer function) is

The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to

The value of int_-1^10 sgn (x -[x])dx is equal to (where, [:] denotes the greatest integer function