Maths C4 - Integration... Help???

So, for complicated reasons, I took Maths A level twice, even though I got an A the first time (and this was before A* was a grade, so A was highest possible).

When I did it the first time, my integration was so-so; I could usually do the questions, but not 100% of the time.

The next year, I was preparing for Cambridge entrance, and one of the things I did was go through all (or nearly all) the integration exercises in Bostock and Chandler. I don't remember exactly how many there were, but we're definitely talking 100s. By the end of that, I could integrate pretty well, and I knew all the trig identities by heart too! The A-level questions were a breeze that year!

But there's no getting round that it was a lot of work and took a lot of time.

I guess it's true what they say, practice really does make perfect!

I just hate how there are so many different ways you need to know how to integrate for particular equations. I'm just about to learn the substitution method but my head is literally going to explode with the methods used in conjunction with the reverse chain rule. I feel like I am never going to remember everything by the time exams come around!

With practise you'll find it a lot easier to spot the methods to use. Like the substitution ones typically follow a certain form, and the same for the other ones. Try writing out a few example integrals for each type and you should see what I mean.

So I've come to the part of the Edexcel C4 Modular Maths Textbook where it states that the trapezium rule can be used for integrals involving some of the new functions met throughout C3 and C4...


I never learnt how to use the trapezium rule using the formula above as I learnt it the way ExamSolutions teaches it! Which is...

Will I be at a disadvantage if I don't know how to use the way the formula is given in the textbook?

But those two are literally the same formulae?

So I've come to the part of the Edexcel C4 Modular Maths Textbook where it states that the trapezium rule can be used for integrals involving some of the new functions met throughout C3 and C4...


I never learnt how to use the trapezium rule using the formula above as I learnt it the way ExamSolutions teaches it! Which is...

Will I be at a disadvantage if I don't know how to use the way the formula is given in the textbook?

I know, but the one in the textbook is confusing in comparison to the way that ExamSolutions suggests how to look at it. The formula from the textbook just looks like a bunch of y's and h's

I know, but the one in the textbook is confusing in comparison to the way that ExamSolutions suggests how to look at it. The formula from the textbook just looks like a bunch of y's and h's

You won't be at a disadvantage, it means the exact same thing. The examsolutions way is the way I learnt it too and I quote it in my exams as it's easier to process when written with actual words.

Well I don't know what to suggest. Practice using that formula I suppose?? That's the formula that will be in your formula booklet so I'd suggest you get to know how to use it. Practice a few questions and you'll be fine with it.

It's only confusing because it is rigorously generalised just as many other things in maths. In the question you are given a,b, and n so there's most of your variables. All you need to do is plug them into the formula where appropriate.

As long as your working is clear and, in essence, applies the trapezium rule, then you're at no disadvantage which one you use, keep in mind that that's the formula in the booklet however just in case you might need to refer to it in an exam.

As others have said, if you remember the formula in words then it's not a huge problem.

But you could get exam questions that refer to the notation used in the formula e.g. $y_1$ so I would recommend at least understanding it.

It really isn't a hard formula. You just need someone to explain what the notation means. If you need help with that, let us know what you do understand from the formula and what you don't.

Can someone explain part 1(e)?
What am I supposed to do with the $sin^3 x$ ?


**EDIT: Don't worry I think I've almost worked this out

Did you get it in the end?

Will I get penalised for my workings here?...

No

Can anyone help me with part (d) ?



So far I've done...
$= \int (cot^2 x - 2 cot x cosec x + cosec^2 x ) dx$

Not quite sure how you got that. Just expand it out, and rewrite $\sin^2(x)$ as a double angle.

Can anyone help me with part (d) ?



So far I've done...
$= \int (cot^2 x - 2 cot x cosec x + cosec^2 x ) dx$