Finding the definite integral of $f(x)=[[x]]$.

Asked Nov 18 '13 at 02:45

Active Nov 18 '13 at 03:23

Viewed 141 times

Here $[[x]]$ shall denote the greatest integer function. Evaluate the definite integral $\int_{-2}^{2}2[[x]]dx$

I'm super confused on this problem, can anybody please help me solve this problem.

P.s.: the $x$ is surrounded by double brackets which I have no idea what they mean.

edited Nov 18 '13 at 03:23

Ana Galois

asked Nov 18 '13 at 02:45

John Beal

1

HINT: Draw the graph and think of the integral as the area under the curve. – Spenser Nov 18 '13 at 02:48
1

I assume you mean you don't know the definition of the greatest integer function. Your text should contain it, but here it is. $[[x]]$ is the (unique) integer $n$ such that $n\leq x< n+1$. It is also known as the floor function. – zibadawa timmy Nov 18 '13 at 02:48
1

A related problem. – Mhenni Benghorbal Nov 18 '13 at 03:17

0 Answers0