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1.
Alright so, Friday's class was all about another method used to solve antiderivatives. It is called integration by parts.
1
2.
We started off with this question:
2
3.
Hmmm... the answer is, yes, but we have to use a different technique. As you can see the method of substitution will not work on this one. That's why we need another technique called integration by parts.
3
4.
4
5.
Now, let us apply that new rule to solve the previous question. First, we need to decide which one is going to be f and g'. The question is how to decide which function will be f ?
5
6.
The answer is, we just need to remember this mnemonic.
6
7.
Now, according to that mnemonic we will have this:
7
8.
Then, we just need to find out the missing pieces required to use the rule of integration by parts. We still need to find f ' and g, so by finding the derivative of f and antidifferentiating g we get this:
8
9.
Now, we are set. We have all the needed pieces to make the rule work. All we need is to substitute the functions.
9
10.
Now all we need is to antidifferentiate this part then we will get our answer, which is:
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11.
After that we practiced on more questions that use application of the rule of integration by parts. In some cases we need to use it more than once, but I'm not going to bother explaining those because there is nothing new, except that you just need to do use the rule again.
11
12.
The rule can be used in antidifferentiating a composite function but, it can also be applied when integrating a single function by considering the function g'(x) to be the factor 1.
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13.
For example: The only thing different here is that we just used function g'(x) to be the factor 1, in order to have two functions.
13
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