00:01
7 .4, problem 26.
00:03
We're dealing with problems here that are solved with integration using trick substitutions.
00:08
What i need to work on first is this radical 1 minus 2x before i can make my substitution, i need to factor the 2 that's in front of the x so i can write this as 2 times 1 half and i'm sorry this was an x squared so 2 times 1 half sorry about that i don't want to make mistakes so this is x squared, this is x squared.
00:37
So factor out the two.
00:39
Try this again.
00:41
One half minus x squared.
00:44
Okay.
00:45
And so now you can see this is just the square root of two times the square root of one half minus x squared.
00:56
So we can write this as the integral.
01:00
So this is going to be one over the square root of two and then one over the square root of one half minus x squared d x now this is in the format for a sign substitution so the substitution that i need is the square root of one -half times the sign so i'm going to let x equal the square root of one -half sine theta and dx is going to be the square root of one -half cosine theta and then one -half minus x squared is one half minus one half sine squared theta.
01:51
So that's one half, one minus sine squared...