# Arc Length of a Conic

Watch
Announcements
#1
Hi,
Could anybody help me with the following question? I have attached the question in my book and my solution so far. But I am stuck and can't figure out how to continue as the integral gets too complicated to integrate. Is there something I am doing wrong or missing? I would be really grateful if anyone could help.
Last edited by Tesla3; 1 year ago
0
1 year ago
#2
(Original post by Tesla3)
Hi,
Could anybody help me with the following question? I have attached the question in my book and my solution so far. But I am stuck and can't figure out how to continue as the integral gets too complicated to integrate. Is there something I am doing wrong or missing? I would be really grateful if anyone could help.
It "says" approximately, which suggest some sort of power series.

Spoiler:
Show

binomials
0
#3
(Original post by ghostwalker)
It "says" approximately, which suggest some sort of power series.

Spoiler:
Show

binomials
Could you please elaborate? like Maclurin Series?
0
1 year ago
#4
(Original post by Tesla3)
Could you please elaborate? like Maclurin Series?
It's in the spoiler of my first post!
0
#5
(Original post by ghostwalker)
It's in the spoiler of my first post!
Can you show how? I am a bit confused......
0
1 year ago
#6
(Original post by Tesla3)
Can you show how? I am a bit confused......
Check your textbook. What's the expansion of ? Then just replace the x and n with the appropriate values. You have two binomials to expand. Have a go.
0
#7
(Original post by ghostwalker)
Check your textbook. What's the expansion of ? Then just replace the x and n with the appropriate values. You have two binomials to expand. Have a go.
I get that the denominator can be expanded using the binomial theorem but what about the numerator? It has three terms e^2 , 1 and 2ecos(theta).
0
#8
After using the binomial theorem I get this........
0
1 year ago
#9
(Original post by Tesla3)
After using the binomial theorem I get this........
Well expanding the square in the denominator hardly qualifies as requiring the full might of the binomial expansion.

Let's rewrite the integrand to make it clearer.

Now try.
0
#10
(Original post by ghostwalker)
Well expanding the square in the denominator hardly qualifies as requiring the full might of the binomial expansion.

Let's rewrite the integrand to make it clearer.

Now try.
wait let me try.....
0
#11
After expansion and multiplying I get something like this. Also I neglect any e terms with power equivalent to 2 or higher. Then I simplify and integrate to get the desired result. Is it okay? ghostwalker
Last edited by Tesla3; 1 year ago
0
1 year ago
#12
(Original post by Tesla3)
After expansion and multiplying I get something like this. Also I neglect any e terms with power equivalent to 2 or higher. Then I simplify and integrate to get the desired result. Is it okay? ghostwalker
Looks fine.

You made a minor slip in the second expansion - should have e^2/2 - but it doesn't effect the final outcome.
1
#13
(Original post by ghostwalker)
Looks fine.

You made a minor slip in the second expansion - should have e^2/2 - but it doesn't effect the final outcome.
Thanks
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

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

### Poll

Join the discussion

#### Poll: What factors affect your mental health most right now? Post-lockdown edition

5.94%
Uncertainty around my education (92)
11.39%
Uncertainty around my future career prospects (83)
10.27%
Lack of purpose or motivation (103)
12.75%
Lack of support system (eg. teachers, counsellors, delays in care) (40)
4.95%
Impact lockdown had on physical health (45)
5.57%
Social worries (incl. loneliness/making friends) (89)
11.01%
Financial worries (54)
6.68%
Concern about myself or my loves ones getting/having been ill (37)
4.58%
Exposure to negative news/social media (51)
6.31%
Difficulty accessing real life entertainment (25)
3.09%
Lack of confidence in making big life decisions (77)
9.53%
Worry about missed opportunities during the pandemic (64)
7.92%