The Student Room Group

A tale of two integrals

A couple of (A-level) integrals for you guys to enjoy! :smile:

1 Problem



2 Problem

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Reply 1
Original post by Indeterminate
A couple of (A-level) integrals for you guys to enjoy! :smile:

1 Problem



2 Problem



I approve
shame I am teaching
Disappointed by the fact that we haven't had any responses yet :cry2:
Original post by Indeterminate
You guys disappoint me :cry2:


I worked on the first one for literally an hour and couldn't get anywhere further than all multiples/orders of cosxs :cry:
Original post by Indeterminate
Disappointed by the fact that we haven't had any responses yet :cry2:


My integration's a bit crap. Something like x=cos2u x = \cos 2u on the 2nd?
Original post by Student403
I worked on the first one for literally an hour and couldn't get anywhere further than all multiples/orders of cosxs :cry:


:console:

Getting rid of the half angles is the key to this one. How good is your trig? :colone:

Original post by 16Characters....
My integration's a bit crap. Something like x=cos2u x = \cos 2u on the 2nd?


Try it by all means :smile:
Original post by Indeterminate
:console:

Getting rid of the half angles is the key to this one. How good is your trig? :colone:



Try it by all means :smile:


I got rid of them all and got down to a large expression just involving a bunch of cosx's multiplied by each other and a few square roots and squares :/
Original post by Student403
I got rid of them all and got down to a large expression just involving a bunch of cosx's multiplied by each other and a few square roots and squares :/


I see. Well I'm sure @Zacken will have a few ideas.

The purpose of this thread is to get you guys talking:biggrin: Think of me as a last resort :tongue:
Reply 8
Original post by 16Characters....
My integration's a bit crap. Something like x=cos2u x = \cos 2u on the 2nd?


Original post by Indeterminate
I see. Well I'm sure @Zacken will have a few ideas.

The purpose of this thread is to get you guys talking:biggrin: Think of me as a last resort :tongue:


I'm thinking u=1+xu = \sqrt{1+x}. :redface:
Reply 9
Re my last post: nopes.
Original post by Zacken
I'm thinking u=1+xu = \sqrt{1+x}. :redface:


You've both made interesting suggestions :biggrin: However, it's not a straightforward, single-substitution integral.

I'd go with @16Characters....myself
Reply 11
Fairly sure I can see how to get the second one out. I'll give it a go soon.

Posted from TSR Mobile
Reply 12
Original post by Indeterminate
You've both made interesting suggestions :biggrin: However, it's not a straightforward, single-substitution integral.

I'd go with @16Characters....myself


Yeah, I realised. :biggrin: - you should totally give difficulty ratings for your integrals. :redface: (*, **, *** perhaps?).
Original post by Zacken
Yeah, I realised. :biggrin: - you should totally give difficulty ratings for your integrals. :redface: (*, **, *** perhaps?).


Haha, I'd say that they're both **

I could do worse :colone:
Reply 14
I'm down to: sin2xsin(x+π4)+1dx\displaystyle \int \frac{-\sin 2x}{\sin \left(x + \frac{\pi}{4}\right) + 1} \, \mathrm{d}x
Original post by Zacken
I'm down to: sin2xsin(x+π4)+1dx\displaystyle \int \frac{-\sin 2x}{\sin \left(x + \frac{\pi}{4}\right) + 1} \, \mathrm{d}x


So far, so good. Time to sort out the trig :biggrin:

Hint:

Spoiler

Reply 16
Original post by Indeterminate
So far, so good. Time to sort out the trig :biggrin:

Hint:

Spoiler



... :cry2: But I moved from \cdots to the collected sine term.

I'm on cos2xsinx+1dx\displaystyle \int \frac{\cos 2x}{\sin x+1} \, \mathrm{d}x right now.
Original post by Zacken
... :cry2: But I moved from \cdots to the collected sine term.

I'm on cos2xsinx+1dx\displaystyle \int \frac{\cos 2x}{\sin x+1} \, \mathrm{d}x right now.


Carry on. Let's see what you get! :biggrin:
Original post by Indeterminate
A couple of (A-level) integrals for you guys to enjoy


Hi, these integrals are beyond me!
I just wanted to say that I think the title of this thread is amazing! I don't know if you did it on purpose or not (you probably did) but it's so clever the qay it's like A tale of two cities :biggrin:

Posted from TSR Mobile
Original post by Matrix123
Hi, these integrals are beyond me!
I just wanted to say that I think the title of this thread is amazing! I don't know if you did it on purpose or not (you probably did) but it's so clever the qay it's like A tale of two cities :biggrin:

Posted from TSR Mobile


Yup :biggrin: I'm quite a fan of Dickens and A Tale of Two Cities is one of my most favourite works of his :awesome:

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