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Will the real TeeEm please stand up!

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Original post by TeeEm
surely you can simplify it further from that line!!!!

I cannot tell if it is correct until you simplify it fully, but it is looking good
(did you see the limits?)


Yeah I edited it afterwards :smile: what limits?
Reply 121
Original post by aersh8
Yeah I edited it afterwards :smile: what limits?


the integral has limits and the answer is in a box at the bottom right
Original post by TeeEm
the integral has limits and the answer is in a box at the bottom right


strange, this is all I can see:
Capture.JPG
Reply 123
Original post by aersh8
strange, this is all I can see:
Capture.JPG


which integral are you doing?

there are 2

the answer you were showing me was almost the answer of the previous one in post 114
(edited 8 years ago)
Original post by TeeEm
which integral are you doing?

there are 2

the answer you were showing me was almost the answer of the previous one in post 114


I'm doing the Lucy one, the Alexandra one had the answer so it was good :smile:
Reply 125
Original post by aersh8
I'm doing the Lucy one, the Alexandra one had the answer so it was good :smile:


I took the answer off now! (I left it by mistake)

The Lucy one is tough in the concentration front.
Original post by TeeEm
I took the answer off now! (I left it by mistake)

The Lucy one is tough in the concentration front.


Ah alright :smile:

Is Lucy meant to have limits though?
Reply 127
Original post by aersh8
Ah alright :smile:

Is Lucy meant to have limits though?


no limits on that

the answer you had before was almost the answer to the one in post 114 without limits.

the answer to the one in post 119 is also a neat log
Reply 128
Original post by aersh8

Spoiler



yes
Original post by TeeEm
yes


Thanks! Couldn't wait till Saturday to find out :P

How do you even come up with these questions?
Reply 130
Original post by aersh8
Thanks! Couldn't wait till Saturday to find out :P

How do you even come up with these questions?


those two are dead easy to make.

think of a disgusting function
differentiate it
then give to students to reverse the order, i.e. integrate

Today I am off and I made 2 very hard integrals, for the mathematicians only, i.e no clues
and I am currently working on a third but it is giving me trouble for the last 2 hours
Original post by TeeEm
those two are dead easy to make.

think of a disgusting function
differentiate it
then give to students to reverse the order, i.e. integrate

Today I am off and I made 2 very hard integrals, for the mathematicians only, i.e no clues
and I am currently working on a third but it is giving me trouble for the last 2 hours


These are really neat when using the substitution though, surely that requires some more thinking?

Are those integrals solve-able using A level maths knowledge? If so please share :biggrin:
Reply 132
the first one I have written a solution in two different ways

the second one one method


the third one I am trying to find a sensible method, because the method I have here involves the most ridiculous partial fractions I ever had to do
Original post by TeeEm
the first one I have written a solution in two different ways

the second one one method


the third one I am trying to find a sensible method, because the method I have here involves the most ridiculous partial fractions I ever had to do


I did the first one - it took ages so I'm 99.9999% I made a careless mistake along the way

Spoiler

Reply 134
Original post by aersh8
I did the first one - it took ages so I'm 99.9999% I made a careless mistake along the way

Spoiler



sorry but it is not correct.
There is no ln(...) in this one
final answer is very simple

do you need a hint?
Original post by TeeEm
sorry but it is not correct.
There is no ln(...) in this one
final answer is very simple

do you need a hint?


I used u = rootx as a substitution to get:

2*integral(1 + (1/(u^2 + 1)) - (2/((u^2 + 1)^2)) du

and then to integrate that I substituted x back in (so multiplied it all by 1/(2rootx) since du = dx/2rootx), split all that into partial fractions and integrated

does that seem like a correct method? I'm pretty sure I made a mistake in the partial fractions bit since I ran out of paper and had to squeeze it all into the bottom of a page

If there's something wrong with this method then may I please have the hint :smile:
Reply 136
Original post by aersh8
I used u = rootx as a substitution to get:

2*integral(1 + (1/(u^2 + 1)) - (2/((u^2 + 1)^2)) du

and then to integrate that I substituted x back in (so multiplied it all by 1/(2rootx) since du = dx/2rootx), split all that into partial fractions and integrated

does that seem like a correct method? I'm pretty sure I made a mistake in the partial fractions bit since I ran out of paper and had to squeeze it all into the bottom of a page

If there's something wrong with this method then may I please have the hint :smile:


The standard way is

u=rootx
then you get partial fractions which are improper, repeated and irreducible!!!!!!
This is very easy to go wrong
Then
you will need to know how to integrate back into an arctan
and then you are done....

Once you achieve the solution in this way then you can see what substitution would clear this mess quicker
Original post by TeeEm
The standard way is

u=rootx
then you get partial fractions which are improper, repeated and irreducible!!!!!!
This is very easy to go wrong
Then
you will need to know how to integrate back into an arctan
and then you are done....

Once you achieve the solution in this way then you can see what substitution would clear this mess quicker

Thanks!
Did I get the first bit right then (the partial fractions in terms of u)?
What do you mean integrate back into an arctan?
Reply 138
Original post by aersh8
Thanks!
Did I get the first bit right then (the partial fractions in terms of u)?
What do you mean integrate back into an arctan?


Your partial fractions are good!!!

see if you can finish it!!
Original post by TeeEm
Your partial fractions are good!!!

see if you can finish it!!


How would you use arctan though?

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