I was looking for a brief explanation as to which of the following functions are Riemann integrable or not.
$f(x):=(1-x^2)^{-1} $if $ x≠ 1 $ and $ x ≠1,$
$f(x):= 0, $ if $ x=1 $ or $ x=-1.$
(Over interval: $[-1,1]$)
I can see that the function is continuous & hence Riemann integrable over $(-1,1)$ but don't know how I can explain that it is over $[-1,1]$. I am thinking I maybe can just say that it is bounded?
Also
$f(x)=\frac{1}{x^2-3x-4},$ over interval $[-3,0]$,
I see in the interval when $x=-1$, $f(x)$ is undefined. Is it acceptable to say that this function is hence not bounded over this interval and hence not Riemann integrable?
No comments:
Post a Comment