Suppose f(x) is the greatest integer function, i.e., f(x) equals the greatest integer less than or equal to . So for example f(2.3) =2, f(4)=4 and f(6.9)=6

Question

 Suppose f(x) is the greatest integer function, i.e., f(x) equals the greatest integer less than or equal to .  So for example f(2.3) =2, f(4)=4 and f(6.9)=6 

find

∫7 𝑓(𝑥)𝑑𝑥.

11

the integral is equal to

Answer 1

Your notation is a bit unclear, but the integral of a step function like this is simply the sum of rectangles made by the ordinate of the step * the abscissa of the beginning of the interval.

No true integration here, simply addition!