Let
f(x)=
{ 1 if -1 < or equal to x<0;
{-1 if 0 < or equal to x < or equal to 1.
Prove that f(x) is integrable on -1 < or equal to x < or equal to 1.
I fail to see how this can be a problem, what do you know about integration?
(what type of integral are we talking about here).
If this is a Riemann integral it is obvious that the integral of is
defined over from a elementary consideration of the Riemann
sums of for partitions of this interval, and that the integral is:
RonL
Okay, for suffiently large .
You want to find,
I will use right endpoints,
But,
Thus,
Note,
(greatest integer).
Thus, the function is 1 for these values.
And it is -1 for after these values.
If is even we have,
Thus, as the limit of the Riemann sum is zero.
If is odd we have,
Thus, as the limit of the Riemann sum is zero.
Thus, the limit is always zero no matter what.