00:01
We want to find an antiderivative for each of these functions here.
00:05
So starting with a, we can just go ahead and apply our anti -derivative.
00:10
And this follows directly from the chart of antiderivatives that they give us.
00:16
So in this case, k is 1 and a is 3.
00:21
So we just go ahead and follow what we have over here.
00:23
So it should be 1 over k, so just 1, natural log of a, which is 3.
00:29
And then we just have our expression again, and we add a constant c.
00:34
Now, so say, tell us to just give a solution as opposed to all possible, we can just let c equal to zero for simplicity, because when we add zero, that term just drops off, and we could just be left with this for one possible antiderivative.
00:52
But you can add any number you want to this, and also get a valid anti -derivative.
01:01
Now let's go on to the next one.
01:04
So again, we're just going to apply the anti -derivative that they tell us in this chapter.
01:11
So in this case, k is negative 1, and a is 2...