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## This Week

In lectures, we finished off chapter 2.

In tutorials we did p.17 Q.1 (d)(f), p.32 Q.1,9, p.36 Q. 7, 8, 12 and p.39 Q. 2, 3.

## Teaching Practise

Be aware that these two weeks are a terrible risk to you falling behind in integration so make serious efforts to either keep up with the work or catch up ASAP: week 4’s lectures.

Note that I will not be scanning up any more of these notes.

## 2 comments

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May 3, 2012 at 10:06 am

Student 13In our notes on page 43 for the autumn exam question why do u let when the integral can be broken up into and so could use as ?

May 3, 2012 at 10:16 am

J.P. McCarthyThe start of section 2.4 explains why choosing should work. However, we can talk more generally and say that the whole time when doing substitutions we are looking for the function-(multiple of-)derivative pattern. We have it here:

.

So is a function (inside another which is fine), and is a multiple of its derivative.

You could do your substitution but it’s a lot longer and harder:

.

The best we can do with is so we get

.

This needs a substitution of the form to get

.

It takes a little work to see that this equals .