This discussion is closed.
Aitch
Badges: 2
Rep:
?
#1
Report Thread starter 14 years ago
#1
Is this method cheating?

P5 Integration Heinemann 3A Q42

"Find the area of the finite region bounded by the curve with equation
x² - y² = 4 and the line x = 5"

For backgound and 2 solutions provided by BCHL85 and Nima, see this

thread first:

http://www.thestudentroom.co.uk/t90907.html

While previously stuck and struggling alone, I decided to try integrating the polar equation instead.

from x² + y² = r² (1)
and 2y² = 2r².sin²θ (2)

you get

4 = x² - y² = (1)-(2) = r²(1-2sin²theta)
so
r² = 4 sec 2θ
½∫r² dθ = ln|sec 2θ + tan 2θ|

θ top limit is given by point where x=5 cuts the hyperbola (y=√21)
so θ = arccos (5 ÷ √46)

θ bottom limit equates to zero.

so enclosed area between 0, initial line, the curve is 3.134
Area of triangle between 0, initial line, (5,√21) is 11.456

Subtract to give 8.322, as before.

Is this cheating? If a polar version produces a better route, is it OK?

I won't say it was quicker, because I made a pig's ear of the

integration of r² to start with, and had to retrace my steps twice!

Aitch
0
dvs
Badges: 10
Rep:
?
#2
Report 14 years ago
#2
Sometimes switching coordinate systems might help a lot with integration, but I wouldn't recommend doing it on your A-level exams. You don't know how competent the person grading your paper is, so he could think you accidentally got the correct answer, and give you almost no marks for your working. I wouldn't risk it.
0
Aitch
Badges: 2
Rep:
?
#3
Report Thread starter 14 years ago
#3
(Original post by dvs)
Sometimes switching coordinate systems might help a lot with integration, but I wouldn't recommend doing it on your A-level exams. You don't know how competent the person grading your paper is, so he could think you accidentally got the correct answer, and give you almost no marks for your working. I wouldn't risk it.
This was my gut feeling!

I felt that, in a way, I was avoiding the question!

Thanks.

Aitch
0
El Stevo
Badges: 1
Rep:
?
#4
Report 14 years ago
#4
if you p5 syllabus (dunno about edexcel, i'm on aqa...) covers integrating polar functions, or any pure module prior to p5 does, then you can use the method. if it doesn't then i'd only use it as a last resort...
0
Yttrium
Badges: 1
Rep:
?
#5
Report 14 years ago
#5
For P5, there aren't many chief examiners (at least not for Edexcel - our maths teacher is one, but only for Decision maths) and she reckons that they're all capable.

You should be able to get credit for extra-specially clever things in P4, P5, P6 - but it's worth sticking to more obvious stuff in P3.

At least, that's what she reckons.
0
X
new posts
Back
to top
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

  • Cardiff Metropolitan University
    Undergraduate Open Day - Llandaff Campus Undergraduate
    Sat, 19 Oct '19
  • Coventry University
    Undergraduate Open Day Undergraduate
    Sat, 19 Oct '19
  • University of Birmingham
    Undergraduate Open Day Undergraduate
    Sat, 19 Oct '19

Why wouldn't you turn to teachers if you were being bullied?

They might tell my parents (24)
6.88%
They might tell the bully (33)
9.46%
I don't think they'd understand (53)
15.19%
It might lead to more bullying (135)
38.68%
There's nothing they could do (104)
29.8%

Watched Threads

View All