Integer part 3

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

Let [x] denote the greatest integer part of a real number x, if M= sum_(n=1)^(40)[(n^(2))/(2)] then M equals

If [x] and (x) are the integral part of x and nearest integer to x then solve (x)[x]=1

If x= (8 + 3 sqrt(7))^(n) , where n is a natural number, power that the integral part of x is an odd integer and also show that x - x^(2) + x[x] = 1 , where [.] denotes the greatest integer function .

Show that the following integers are cubes of negative integers. Also find the integer whose cube is the given integer. -5832 (ii) -2744000

Solve the following equations x^(2)-3-{x}=0 where [x] denotes the greatest integer and {x} fractional part.

If the sum of the last 3 integers in a set of 6 consecutive integers is 624, what is the sum of the first 3 integers of the set?

If[.] and {.} denote greatest integer and fractional part functions respectively, then the period of f(x) = e^(sin 3pi{x} + tan pi [x]) is

If the sum of the last 3 integers in a set of 7 consecutive integers is 258, what is the sum of the first 4 integers?

The value of int_(0)^(|x|){x} dx (where [*] and {*} denotes greatest integer and fraction part function respectively) is