00:01
So this type of integration is called a definite integral because you're going to be plugging in these two numbers.
00:08
And when you have something that you want to integrate, but it has addition or subtraction, you can actually split it up into two things.
00:15
So we can split this up into the integral of x dx plus the integral of 2 over x dx.
00:25
And then we still have going from 6 to 7 on both of them.
00:30
Okay, the next step for this one would be to apply something called the power rule.
00:36
So what we do is, well, this has a power of one.
00:39
What we do is we add one to this power and then we divide by that new power.
00:46
And you're going to integrate this from six to seven.
00:50
And then for this second integral, well, let's first take out the constant in front.
00:57
So we have one over x dx from six.
01:00
6 to 7.
01:02
And this is actually a well -known integral.
01:05
This is going to be ln of x.
01:07
So we have x squared over 2 from 6 to 7 plus 2 times and then we said this was ln of x, evaluated from 6 to 7.
01:21
Now what does this bar notation mean? it means that we plug in the first one and then we subtract the second one...