00:01
We want to integrate this function.
00:03
There are many ways to do it, but for this topic, we are to use a substitution and followed by integration by parts.
00:12
So let me let s be square root 1 minus x.
00:19
So the s over the x will be half, 1 minus x to power minus half and then minus 1.
00:32
So we know that the s will be minus 1 over 2 root 1 minus x the x.
00:48
So this one is 1 over minus 2.
00:51
Now square root of 1 minus x is s the x.
00:58
So the x is actually minus 2 s the s.
01:04
Now, since s is square root of 1 minus x, when x is 0, sorry, when x is 0, my s will be sucked into here, 1 minus 0 square root, my s will be 1.
01:24
When x is 1, my s will be 0.
01:29
Now, squaring both sides, i'll have x square equals to 1 minus x.
01:33
So my x is 1 minus s square.
01:36
So now i'm ready to do substitution...