00:01
In order to evaluate this definite integral, we first find the definite integral of each component.
00:06
So we're going to do one -half to one of three over one plus two t d t.
00:12
So that's this first component here.
00:15
Now the integral of this is just going to be three times ln or three -half, sorry, ln of 1 plus 2t.
00:26
And we're going from one -half to one.
00:28
So plugging in one first, we get three -half.
00:31
And then when we add or do one here, we get 1 plus 3.
00:38
So we get ln of 3 and then minus.
00:42
And then we have three halves ln of when we do one half here, we get 1 plus 1.
00:50
So ln of 2.
00:53
And then since we have a three halves on both of them, we can pull that out.
00:57
And then so we have ln or three halves ln of 3 minus ln of 2...