# P5 Integration - Is this cheating?Watch

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#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

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

Aitch
0
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
#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
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
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.
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