00:01
For this problem, we are asked to evaluate the given definite integral.
00:04
So it's from 0 to 1 half of dx over 4x squared plus 1 to the power of 3 over 2.
00:09
So we have that that integral, let's see here.
00:14
The first, actually, i won't rewrite it immediately.
00:17
The first step that we would take is recognize that we have an integral in the form of 1 over the square root of bx squared plus a, which means that our standard trigonometric substitution here would be x equals root a over root b times tan of u so in this case our direct substitution is going to be x equals 1 over 2 tan of u which then means that d x by d u will be equal to 1 half secant squared of u which means that when we rewrite our expression now after having made that substitution.
01:09
Now i'll note that at the moment, i'm just going to treat this as an indefinite integral.
01:14
This would become just 1 over 2 secant of u, d .u.
01:19
Actually, that's a little bit skipping ahead, just a little bit too much...