The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Implicit equations help

I'm stuck on question 4


Posted from TSR Mobile
ImageUploadedByStudent Room1364332029.929770.jpg144.5KB

Scroll to see replies

Reply 1
Avatar for SDavis123
SDavis123
OP
15
And this is as far as I've got


Posted from TSR Mobile
ImageUploadedByStudent Room1364332114.486291.jpg153.9KB
Oh that's horrible!

Really!

You have separated the variables correctly but the next line is just drivel. Try substituting a couple of numbers and you will agree.

Integrate the y term by recognising a logarithmic integral and the x term by making a substitution for the denominator or by expressing it in divided out form.
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by SDavis123
And this is as far as I've got


Posted from TSR Mobile


Line 1 = good

Line 2 = rubbish

xx−1≠1−x\dfrac{x}{x-1} \not= 1-x

Ditto the y side being incorrect
Reply 4
Avatar for SDavis123
SDavis123
OP
15
Original post by Mr M
Oh that's horrible!

Really!

You have separated the variables correctly but the next line is just drivel. Try substituting a couple of numbers and you will agree.

Integrate the y term by recognising a logarithmic integral and the x term by making a substitution for the denominator or by expressing it in divided out form.


Ah yes I see what you mean so take the 2 out of the y bit to make the top differential of the bottom so you'll get ln(y^2 +1) ?


Posted from TSR Mobile
To explain your misconception:

ab+c≠ab+ac\displaystyle \frac{a}{b+c} \neq \frac{a}{b} + \frac{a}{c}
Original post by SDavis123
Ah yes I see what you mean so take the 2 out of the y bit to make the top differential of the bottom so you'll get ln(y^2 +1) ?


Posted from TSR Mobile


Sort of.

You need to deal with the 2 you just threw away.
Reply 7
Avatar for SDavis123
SDavis123
OP
15
Ah yh sorry, (1/2)(ln(y^2 + 1))


Posted from TSR Mobile
Original post by SDavis123
Ah yh sorry, (1/2)(ln(y^2 + 1))


Posted from TSR Mobile


Yes.
Reply 9
Avatar for SDavis123
SDavis123
OP
15
Original post by Mr M
Yes.



I'm not sure on the x part but I said

x/(x-1)=x(x-1)^-1

And when I integrate that I get

((-x^2)/4).(x-1) that right?


Posted from TSR Mobile
Original post by SDavis123
I'm not sure on the x part but I said

x/(x-1)=x(x-1)^-1

And when I integrate that I get

((-x^2)/4).(x-1) that right?


Posted from TSR Mobile


You seem to be making up your own integration rules now.

xx−1=x−1+1x−1=1+1x−1\displaystyle \frac{x}{x-1}=\frac{x-1+1}{x-1}=1+\frac{1}{x-1} which I hope you can integrate.
Reply 11
Avatar for SDavis123
SDavis123
OP
15
Original post by Mr M
You seem to be making up your own integration rules now.

xx−1=x−1+1x−1=1+1x−1\displaystyle \frac{x}{x-1}=\frac{x-1+1}{x-1}=1+\frac{1}{x-1} which I hope you can integrate.


Ermmm ok haha but how did you get

x/(x-1)=(x-1+1)/(x-1) ?


Posted from TSR Mobile
Original post by SDavis123
Ermmm ok haha but how did you get

x/(x-1)=(x-1+1)/(x-1) ?


Posted from TSR Mobile


Because x=x−1+1x = x - 1 + 1
Reply 13
Avatar for davros
davros
16
Original post by SDavis123
Ermmm ok haha but how did you get

x/(x-1)=(x-1+1)/(x-1) ?


Posted from TSR Mobile


Because x-1+1 = x ???

Edit: SNAP!
Original post by davros
Because x-1+1 = x ???


Snap!

Now your edit made my snap look stupid!
(edited 11 years ago)
Reply 15
Avatar for SDavis123
SDavis123
OP
15
Original post by Mr M
Because x=x−1+1x = x - 1 + 1


Ah yh obviously can't believe I didn't see that haha


Posted from TSR Mobile
Reply 16
Avatar for davros
davros
16
Original post by Mr M
Snap!

Now your edit made my snap look stupid!


I'm trying to write maths while watching the football. I should stop now before I write something stupid!
Reply 17
Avatar for SDavis123
SDavis123
OP
15
Original post by davros
I'm trying to write maths while watching the football. I should stop now before I write something stupid!


Football? And there was me thinking mathematicians were clever :tongue:

And what's the next move after



Posted from TSR Mobile
ImageUploadedByStudent Room1364334426.610457.jpg195.7KB
Original post by SDavis123
Football? And there was me thinking mathematicians were clever :tongue:

And what's the next move after



Posted from TSR Mobile


Integrate it - come on this is getting a bit painful!
Reply 19
Avatar for SDavis123
SDavis123
OP
15
Original post by Mr M
Integrate it - come on this is getting a bit painful!


Yh I did, did you see the picture?


Posted from TSR Mobile

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you