How to integrate greatest integer function
$$\int\lfloor x\rfloor \, dx$$
I don't have any idea how to integrate greatest integer function, only have idea about the function viz. If $x = 1.5$ then the value of function will be $2$.
Request you to please elaborate on this, I will be grateful to you.
Thanks in advance.
Best Answer
Hint: Break up into three integrals, (i) $0$ to $1$; (ii) $1$ to $\sqrt{2}$; (iii) the rest. Each will be quick.
To see why this works, plot $\lfloor x^2\rfloor$ in our interval. You will get a staircase pattern.