I am lost Watch

batboy
Badges: 0
Rep:
?
#1
Report Thread starter 11 years ago
#1
Hey guys,

Me again.

Stupid old me.

Here is a past paper question that I can't seem to get out. I tried integration by parts but the mark scheme suggests using substitution. Now I know substitution but I can't just figure out how to use it here.

Sometimes I feel so dumb.
Attached files
0
quote
reply
nota bene
Badges: 13
Rep:
?
#2
Report 11 years ago
#2
Maybe keep in mind that 1+t^2=sec^2
0
quote
reply
batboy
Badges: 0
Rep:
?
#3
Report Thread starter 11 years ago
#3
Yup,

I know that identity.

But how do I use that?
0
quote
reply
studienka
Badges: 1
Rep:
?
#4
Report 11 years ago
#4
Hope this helps
Attached files
0
quote
reply
nota bene
Badges: 13
Rep:
?
#5
Report 11 years ago
#5
Perform the substitution, and get sec^4 in the denominator (which I assume you've got to), then the way I did is probably not the easiest (if it is correct!), but try dividing through sec^2 and then by cos^2 and see what you get, I'm doing this without paper and pen so may be making algebraic slips.

Remember cos^2(x)-sin^2(x)=cos(2x)
0
quote
reply
batboy
Badges: 0
Rep:
?
#6
Report Thread starter 11 years ago
#6
Hey martinkings

Thanks for the attachement. However, I cannot see the workings on the page - they are giving me some quicktime error.

May I ask what it is you used? Quicktime? What do I need to download to make this work?

This is another attachment - I think this has the solution. What I am concerned with is the logic when changing the variable. I read 2 or three pages on the matter and I made this. Is my logic okay? Is this how we are supposed to do this stupid change of variable thing?

Hit me back guys (especially you martinkings - I am anxious to know what format you used. I use microsoft's equation editor).
Attached files
0
quote
reply
studienka
Badges: 1
Rep:
?
#7
Report 11 years ago
#7
It's a long story about going abroad and forgetting my laptop - but I'm using a Mac at the moment, and I've just used word on it, I simply used a latex program and dragged the pics into the doc.

It looks fine from my side - but if anyone out there uses a word and a mac - tell me what to do.
0
quote
reply
nota bene
Badges: 13
Rep:
?
#8
Report 11 years ago
#8
(Original post by batboy)
This is another attachment - I think this has the solution. What I am concerned with is the logic when changing the variable. I read 2 or three pages on the matter and I made this. Is my logic okay? Is this how we are supposed to do this stupid change of variable thing?
Sorry I don't follow your working...


I do \frac{dx}{d\theta}=sec^2( \theta) and then subbing that back we have \frac{1-tan^2(\theta)}{sec^2(theta)} Divide through sec^2(theta) and get cos^2(\theta)-sin^2(\theta)=cos(2\theta).
0
quote
reply
batboy
Badges: 0
Rep:
?
#9
Report Thread starter 11 years ago
#9
Hmmm....

Why would we do that subbing back into the expression?
0
quote
reply
Mitch87
Badges: 0
Rep:
?
#10
Report 11 years ago
#10
Hope this helps...
Attached files
0
quote
reply
batboy
Badges: 0
Rep:
?
#11
Report Thread starter 11 years ago
#11
OOOOOOOOOOOOOOOOOOOH!

I never thought about it like that.

correct me if I am wrong but we are using this thing:

F(u) * du/dx = F(u) du

?
0
quote
reply
Mitch87
Badges: 0
Rep:
?
#12
Report 11 years ago
#12
I'm not entirely sure what you mean with that F(u)....

I assume you're on about changing dx to du/d(theta)?
0
quote
reply
batboy
Badges: 0
Rep:
?
#13
Report Thread starter 11 years ago
#13
This is an identity my maths text (bostock chandler) has.

Is this what we have to "keep in mind" as we change a variable (I am still trying to understand the concept behind this change of variable thing.)
Attached files
0
quote
reply
Mitch87
Badges: 0
Rep:
?
#14
Report 11 years ago
#14
Forget these ‘identities,’ you just need to remember:

When you use a substitution, you’re saying let x (or whatever) = some other variable; you therefore need to change what you’re integrating with respect to also, in order for it to ‘balance’ if you like.

The original question was ‘dx’ – which you know means integrate with respect to x. If you now say that x = tan u, you need to integrate with respect to the new variable, u – hence you need dx to become du.

So in this case, it was x = tanθ, thus we need dθ instead of dx.

x = tanθ
dx/dθ = sec2θ

This is what you need to re-arrange like any other equation to make ‘dθ’ the subject in order to replace the dx in the original integral.
I’m not sure if I’ve made that very clear or been as mathematically accurate as need be, but I hope it helps...
0
quote
reply
generalebriety
Badges: 14
Rep:
?
#15
Report 11 years ago
#15
(Original post by Paul Mitchell)
x = tanθ
dx/dθ = sec2θ
Of course, you mean dx/dθ = sec2θ.
0
quote
reply
Mitch87
Badges: 0
Rep:
?
#16
Report 11 years ago
#16
Indeed. I pasted from word & 4got the '^'. Sadly I cannot get proper maths lingo 2 work on here. hmm...
0
quote
reply
generalebriety
Badges: 14
Rep:
?
#17
Report 11 years ago
#17
Use the [latex][/latex] tags, along with http://math.ucsd.edu/~jeggers/latex/...athematical%22. That should help. :p:

So, \displaystyle\frac{\text{d}x}{\t  ext{d}\theta} = \sec^2 \theta .
0
quote
reply
batboy
Badges: 0
Rep:
?
#18
Report Thread starter 11 years ago
#18
Got you there Paul Mitchell.

That explanation was concise and clear. As a matter of fact, I believe it was this identity that was causing my confusion in the first place; I used your method on some of the other advanced integration in my text and everything seems to work out fine.

Thumbs up!

All that maths made me hungry.
What do the English much on when they figured out a new mathematical technique?
0
quote
reply
generalebriety
Badges: 14
Rep:
?
#19
Report 11 years ago
#19
(Original post by batboy)
What do the English much on when they figured out a new mathematical technique?
Erm. Fish and chips?
0
quote
reply
batboy
Badges: 0
Rep:
?
#20
Report Thread starter 11 years ago
#20
Where are my manners?

Thanks guys for all your help.
With you guys I am sure I can pull of an A.
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19

Were you ever put in isolation at school?

Yes (221)
28.01%
No (568)
71.99%

Watched Threads

View All