Turn on thread page Beta
    • Thread Starter
    Offline

    15
    ReputationRep:
    Sketch, in the same diagram, the curves with equations r=3cosθ and r=1+cosθ and find the area of the region lying inside both curves.
    I get the integral(s) required for the area to be that attached, and evaluate it to get 7pi/2. However, the book gives the answer as 5pi/4.
    Am i making a mistake somewhere? Thanks.
    Attached Images
     
    Offline

    0
    ReputationRep:
    (Original post by Gaz031)
    Sketch, in the same diagram, the curves with equations r=3cosθ and r=1+cosθ and find the area of the region lying inside both curves.
    I get the integral(s) required for the area to be that attached, and evaluate it to get 7pi/2. However, the book gives the answer as 5pi/4.
    Am i making a mistake somewhere? Thanks.
    From the integral that you've derived, 7pi/2 is defintely the right answer.
    Either the book is wrong, which often does happen, or you need to consider and check your integral(s) again, or even the limits of the integrals.
    Offline

    0
    ReputationRep:
    no - i'm getting 15 pi/12 = 5pi/4 a^2

    check your integration - i think your limits are on the wrong equations

    i got limits of pi to pi/3 for the (1+cos)^2 eqtn and between pi/3 and 0 for the 3cos eqtn

    phil
    Offline

    0
    ReputationRep:
    (Original post by Gaz031)
    Sketch, in the same diagram, the curves with equations r=3cosθ and r=1+cosθ and find the area of the region lying inside both curves.
    I get the integral(s) required for the area to be that attached, and evaluate it to get 7pi/2. However, the book gives the answer as 5pi/4.
    Am i making a mistake somewhere? Thanks.
    my book has answer of 5pi/8 a^2 (this is qeutsion 37 b in rewiew exercise isn't it? :confused:
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by Phil23)
    my book has answer of 5pi/8 a^2 (this is qeutsion 37 b in rewiew exercise isn't it? :confused:
    No it's question 9 of review exercise 2.
    • Thread Starter
    Offline

    15
    ReputationRep:
    i got limits of pi to pi/3 for the (1+cos)^2 eqtn and between pi/3 and 0 for the 3cos eqtn
    phil
    Thanks for trying to help but I don't see why that could be the case.
    The 1+cost curve is 'smaller' for 0<theta<pi/3, as it is all inside the 3cost curve while the 3cost curve is 'smaller' for pi/3<t<pi.
    If I swap the limits around I get 5pi/2.
    Thanks for any help.
    Offline

    8
    ReputationRep:
    Does this help?
    Attached Images
     
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by Fermat)
    Does this help?
    Aaah the upper limit on the second integral should have been pi/2 instead of pi! Thanks that helps a lot.
    I didn't think it would make any real difference as the r=3cosθ curve doesn't have any area for 3pi/2>θ>pi/2, where has the extra area come from? Is a point where r<0 considered to be a point on the opposite side of the pole?
    Offline

    8
    ReputationRep:
    (Original post by Gaz031)
    Aaah the upper limit on the second integral should have been pi/2 instead of pi! Thanks that helps a lot.
    I didn't think it would make any real difference as the r=3cosθ curve doesn't have any area for 3pi/2>θ>pi/2, where has the extra area come from? Is a point where r<0 considered to be a point on the opposite side of the pole?
    Taking the limits from 0 -> pi/2 does the upper half-circle.
    The lower half-circle comes from pi/2 -> pi.

    It looks like your supposition is correct: -ve r comes out on the other side of the pole!

    Edit: I got those curves using graphmatica with limits.
    Attached Images
     
    Offline

    0
    ReputationRep:
    i'm lost - where did pi/2 come from?
    Offline

    8
    ReputationRep:
    (Original post by Phil23)
    i'm lost - where did pi/2 come from?
    mmm.

    If you plot r = [email protected] with values of @ from 0 to pi/2 then you'll get the half-circle shown in the attachment above.

    Is that what you meant?
 
 
 
Turn on thread page Beta
Updated: June 11, 2005
The home of Results and Clearing

2,603

people online now

1,567,000

students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
Poll
How are you feeling about GCSE results day?
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.