Consider the following for the two (02) items that follow: Let f(x) = [x^2] , where [ ] is the greatest integer function. What is _ 2 ^ 3 f(x) , dx equal to?

Step-by-step solution

Given f(x) = [x^2] . The limits of integration are from x = 2 to x = 3 . For x ( 2 , 3 ) , the value of x^2 lies in the interval (2, 3) . Therefore, the greatest integer function [x^2] = 2 . The integral is given by: _ 2 ^ 3 f(x) , dx = _ 2 ^ 3 [x^2] , dx = _ 2 ^ 3 2 , dx = 2[x]_ 2 ^ 3 = 2( 3 - 2 )