Turn on thread page Beta
    • Thread Starter
    Offline

    6
    ReputationRep:
    An ellipse has the following parametric equations;

    x = 5cosθ and y= 4sinθ

    (b) by integration find the area enclosed by the ellipse. (4 marks)

    I get to an equation, integrate it, and get to the stage where I stick in the definite integrals, but then get confuddled about how the whole thing works, needing to multiply by 2 et cetera (centre of ellipse at origin).

    I will not say what the answer is, and I will just look at the method of the person who comes up with the correct answer (explaining the last bit thoroughly :p: )

    Thankyou
    Offline

    0
    ReputationRep:
    does this look right? Ok this is take 2

    Offline

    2
    ReputationRep:
    Theres a 99% chance of this being wrong but I get 20 pi.
    Offline

    2
    ReputationRep:
    (Original post by KAISER_MOLE)
    An ellipse has the following parametric equations;

    x = 5cosθ and y= 4sinθ

    (b) by integration find the area enclosed by the ellipse. (4 marks)
    Right I'll have a quick go.

    x = 5cosθ, y = 4sinθ.

    dx/dθ = - 5sinθ

    ∫y(dx/dθ)dθ = Area

    => ∫{(4sinθ)(-5sinθ)}dθ

    => ∫{-20sin²θ}dθ

    Recall: 1 - 2sin²θ = cos2θ

    ==> sin²θ = ½ -½cos2θ

    => -20∫{½ -½cos2θ}dθ

    => -20{½θ + ¼sin2θ}dθ

    Now limits (don't work very well in theis text box) but between 0 and pi/2:

    => -20{ [pi/4] - [ 0 ] } => 5pi

    => To give full area across 4 quadrants times by 4 ==> 20pi.
    Offline

    0
    ReputationRep:
    (Original post by samdavyson)
    Working on it.
    Ye i was totally wrong first, second, third times. Fourth time lucky Im really bad at the basics
    • Thread Starter
    Offline

    6
    ReputationRep:
    there is also a 1 % chance of you be right ljfrugn :p: can you show how you got this value please?
    Offline

    0
    ReputationRep:
    (Original post by KAISER_MOLE)
    there is also a 1 % chance of you be right ljfrugn :p: can you show how you got this value please?
    look up i ammended my post
    Offline

    2
    ReputationRep:
    (Original post by Syncman)
    Ye i was totally wrong first, second, third times. Fourth time lucky Im really bad at the basics
    How do you integrate the sin²theta ?

    Which identity is that?

    EDIT: I've got it I think.
    Offline

    2
    ReputationRep:
    You use cos2 theta = 1 - 2 sin^2 theta.
    Offline

    0
    ReputationRep:
    o jus learnt the integral.
    But i suppose sin²x = (1/2)-(1/2)cos(2x) ?
    from cos2x = 1 - 2sin²x
    Offline

    2
    ReputationRep:
    I did it slightly differently, I will post it in a min.

    EDIT: Well, I can't figure out MathType :mad:.
    Offline

    2
    ReputationRep:
    (Original post by Syncman)
    o jus learnt the integral.
    But i suppose sin²x = (1/2)-(1/2)cos(2x) ?
    from cos2x = 1 - 2sin²x
    Got you.

    I was just confused as you wrote the integral as ... (sinxcosx)/2 which is the same as what I have now got ... (sin2x)/4.
    Offline

    0
    ReputationRep:
    (Original post by samdavyson)
    Got you.

    I was just confused as you wrote the integral as ... (sinxcosx)/2 which is the same as what I have now got ... (sin2x)/4.
    ye i should have a minus sign in there doesnt matter in this case though.
    Offline

    2
    ReputationRep:
    (Original post by Syncman)
    ye i should have a minus sign in there doesnt matter in this case though.
    You doing C4 in a few Tuesday's time (28th) ?


    I need some serious revision.
    Offline

    2
    ReputationRep:
    (Original post by ljfrugn)
    I did it slightly differently, I will post it in a min.

    EDIT: Well, I can't figure out MathType :mad:.
    It is a bit of an irritation.
    Offline

    0
    ReputationRep:
    (Original post by samdavyson)
    You doing C4 in a few Tuesday's time (28th) ?


    I need some serious revision.
    nope i doin P5
    Offline

    2
    ReputationRep:
    (Original post by Syncman)
    nope i doin P5
    Well Good Luck with it!

    I get that pleasure ( :rolleyes: ) next year.
    • Thread Starter
    Offline

    6
    ReputationRep:
    Cheers all, it is that four quadrant bit at the end which gave me a little stumping
 
 
 
Turn on thread page Beta
Updated: June 14, 2005
The home of Results and Clearing

2,816

people online now

1,567,000

students helped last year

University open days

  1. SAE Institute
    Animation, Audio, Film, Games, Music, Business, Web Further education
    Thu, 16 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  3. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
Poll
Do you want your parents to be with you when you collect your A-level results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.