00:01
Ok, so let's compute the integral from negative 2 to 0 of x squared plus x in the x.
00:09
Well, this one is going to be a limit as n goes to infinity of rn, a right -hand point riemann sum.
00:17
Now, let's compute rn.
00:21
Well, this one is the length of this interval divided by n, so 2 over n, multiplied by a sum with i running from 1 up to n, old.
00:33
This function here, f of x, evaluated that negative 2 plus 2i over n, perfect.
00:44
So we get 2 over n multiplied by a sum with i running from 1 up to n, old.
00:52
This guy squared, which is 4 minus 8i over n plus 4i squared over n squared, plus x, so minus 2 plus 2i over n, perfect.
01:14
Ok, now let's simplify.
01:19
Well, we have 2 over n multiplied by a sum with i running from 1 up to n, old.
01:27
Ok, 4 minus 2, so 2, plus 2 over n multiplied by a sum with i running from 1 up to n, old, 4i squared over n squared.
01:45
So we can write 8 over n cubed, multiplied by a sum with i running from 1 up to n, old, i squared, perfect.
01:58
Finally, we have negative 12 over n squared, multiplied by a sum with i running from 1 up to n, old, i...