00:02
We're given the error function, which is used in probability, statistics, and engineering.
00:08
The error function is defined to be 2 over the square root of pi times the integral from 0 to x of e to the negative t squared d t.
00:25
In part a, we're asked to show that the integral from a to b of e to the negative t squared dt can be written in terms of error functions.
00:42
So the integral from a to b of e to the negative t squared d t.
00:50
Well, we can rewrite this as the integral from a integral from a, 0 to b of e to the negative t squared dt plus the integral from a to 0 of e to the negative t squared dt.
01:26
Using integral properties, we can rewrite this as integral from 0 to b.
01:37
In fact, i'll write this as root pi over 2 times 2 over root 1 % to 2 over root pi to a integral from 0 to b of e to the negative t squared d t, minus 2 over root pi times the integral from 0 to a of e to the negative t squared d t...