Struggling with A2 integration

I am having a really hard time doing integration, I thought A2 differentiation was tough enough but A2 integration showed me it only gets worse.

My teacher teaches 1 subtopic in each lesson, so if I have a double, it'll be 2 subtopics in less than 2 hours, I really can't do it. I haven't understood the last subtopic and they're already rushing through the next one.

My friends who do further maths seem to be coping fine with their timetable and I'm flopping with just 3-4 subtopics per week.

I don't even know what I'm struggling with anymore, we're nearly finished with whole of chapter 11 in the Edexcel maths textbook and I have no clue in what I've been doing for the past few weeks.

Does anyone have time where I can pm them some questions?
I'm honestly really dumb when it comes to maths so it will probably take loads of explaining for me to get it (sorry).

Comment or pm me if you can help a bit, I'll really appreciate it!

You can post any questions (and the work you’ve done so far on them) here and we can try and help

(On PM you can’t attach pictures and doing it on a thread means you’ll get help quicker)

You can post any questions (and the work you’ve done so far on them) here and we can try and help

(On PM you can’t attach pictures and doing it on a thread means you’ll get help quicker)

After working out the u limits and expressing the integral in terms of u and du, you can "forget" about the original version in terms of x. So the limits in the second half of the solution are sqrt(2) and 1, as shown in the solution.

The transformed integral has "u" as the horizontal axis, and you want to find the area between the function f(u) and the u axis.

Also sorry, what do you mean by transformed integrals (I probably should know but unfortunately I don't...)?

Oh I see, by forgetting do you mean I can just sub in root 2 into the u version of the integral?
I've realised if I sub root 2 into u^6/3, I get 8/3 like if I subbed ln4 into the x version.

Also sorry, what do you mean by transformed integrals (I probably should know but unfortunately I don't...)? I think our class did areas and curves last lesson but I'm still struggling with these so haven't got around to those exercises yet

it just means the integral after you have changed the variable. you do not need to draw a picture or anything.

Yes. The integration problem has been transformed from x-space to u-space, via the substitution. I used "transformed" to make clear they're, x&u, different variables.

Yes. The integration problem has been transformed from x-space to u-space, via the substitution. I used "transformed" to make clear they're, x&u, different variables.

this makes it sound much too complicated for an A level student

16ln(sqrt(2)) - 16ln(1)
The root is important.

Ah yes I was looking at my x-version again sorry.


But I still don't know how it goes to 8ln2 though?

ln(1) =...
ln(2^(1/2)) = ...

I still don't quite understand what the second line is...