# Parametric Equations

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I'm struggling to understand some of part d on question 3 in this paper:

http://www.madasmaths.com/archive/iy...apers/c4_y.pdf

I have looked at the solutions but I'm still confused:

http://www.madasmaths.com/archive/iy..._solutions.pdf

I don't get why you have to find the direction of the curve, and why the curve is being integrated between A and B instead of A and E to find the area.

Thanks for any help!

http://www.madasmaths.com/archive/iy...apers/c4_y.pdf

I have looked at the solutions but I'm still confused:

http://www.madasmaths.com/archive/iy..._solutions.pdf

I don't get why you have to find the direction of the curve, and why the curve is being integrated between A and B instead of A and E to find the area.

Thanks for any help!

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#2

(Original post by

I'm struggling to understand some of part d on question 3 in this paper:

http://www.madasmaths.com/archive/iy...apers/c4_y.pdf

I have looked at the solutions but I'm still confused:

http://www.madasmaths.com/archive/iy..._solutions.pdf

I don't get why you have to find the direction of the curve, and why the curve is being integrated between A and B instead of A and E to find the area.

Thanks for any help!

**PhyM23**)I'm struggling to understand some of part d on question 3 in this paper:

http://www.madasmaths.com/archive/iy...apers/c4_y.pdf

I have looked at the solutions but I'm still confused:

http://www.madasmaths.com/archive/iy..._solutions.pdf

I don't get why you have to find the direction of the curve, and why the curve is being integrated between A and B instead of A and E to find the area.

Thanks for any help!

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(Original post by

Do you realize this is a very hard paper only to be used as extension?

**TeeEm**)Do you realize this is a very hard paper only to be used as extension?

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#4

(Original post by

I do yes - I want to tackle harder questions to really test my understanding of the material to make completing the normal questions easier.

**PhyM23**)I do yes - I want to tackle harder questions to really test my understanding of the material to make completing the normal questions easier.

I need to look at the question and the solution.

I hope I can do it

(I have not revised parametrics)

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(Original post by

I need to look at the question and the solution.

I hope I can do it

(I have not revised parametrics)

**TeeEm**)I need to look at the question and the solution.

I hope I can do it

(I have not revised parametrics)

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#6

(Original post by

Thank you very much. I really appreciate your help

**PhyM23**)Thank you very much. I really appreciate your help

The area is swept in Cartesian from left to right, hence the limits

or if this further does not answer your question

do it from

theta = 2pi/3 to theta = zero

then subtract

from theta = -2pi/3 to theta =0

Any good?

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(Original post by

the direction of the curve, as theta increases is marked in the diagram at the beginning.

The area is swept in Cartesian from left to right, hence the limits

or if this further does not answer your question

do it from

theta = 2pi/3 to theta = zero

then subtract

from theta = -2pi/3 to theta =0

Any good?

**TeeEm**)the direction of the curve, as theta increases is marked in the diagram at the beginning.

The area is swept in Cartesian from left to right, hence the limits

or if this further does not answer your question

do it from

theta = 2pi/3 to theta = zero

then subtract

from theta = -2pi/3 to theta =0

Any good?

Why isn't the area just equal to the integral between theta=0 and theta=2pi/3?

What do you mean by 'the area is swept left to right'

Why does the direction of the curve matter?

Where did the -2pi/3 come from in the second part of your answer?

I apologise if some/all of these questions are stupid. This question seems to contain everything about PEs that confuses me, so understanding this fully would help me greatly.

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#8

(Original post by

I'm sorry but I am still confused

Why isn't the area just equal to the integral between theta=0 and theta=2pi/3?

What do you mean by 'the area is swept left to right'

Why does the direction of the curve matter?

Where did the -2pi/3 come from in the second part of your answer?

I apologise if some/all of these questions are stupid. This question seems to contain everything about PEs that confuses me, so understanding this fully would help me greatly.

**PhyM23**)I'm sorry but I am still confused

Why isn't the area just equal to the integral between theta=0 and theta=2pi/3?

What do you mean by 'the area is swept left to right'

Why does the direction of the curve matter?

Where did the -2pi/3 come from in the second part of your answer?

I apologise if some/all of these questions are stupid. This question seems to contain everything about PEs that confuses me, so understanding this fully would help me greatly.

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(Original post by

To find the area between the curve and the x axis you need to integrate from left to right so when it come to the limits from the smaller x to the larger x

**TeeEm**)To find the area between the curve and the x axis you need to integrate from left to right so when it come to the limits from the smaller x to the larger x

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#10

(Original post by

Why do you integrate from left to right? I thought you found the area with the greater cartesian limit on the top of the integral and the smaller limit on the bottom. Does it depend on the circumstance?

**PhyM23**)Why do you integrate from left to right? I thought you found the area with the greater cartesian limit on the top of the integral and the smaller limit on the bottom. Does it depend on the circumstance?

But these are the

**parametric limits**which match these Cartesian limits

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(Original post by

So we agree! Cartesian limits!

But these are the

**TeeEm**)So we agree! Cartesian limits!

But these are the

**parametric limits**which match these Cartesian limits
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#12

(Original post by

Oh I see in the solutions the parametric limits were initially the other way round to what they are in the answer. But why were they flipped?

**PhyM23**)Oh I see in the solutions the parametric limits were initially the other way round to what they are in the answer. But why were they flipped?

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(Original post by

Do you know that if you reverse the limits you generate a minus?

**TeeEm**)Do you know that if you reverse the limits you generate a minus?

http://tutorial.math.lamar.edu/Class.../ParaArea.aspx

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#14

(Original post by

I do yes. So did you flip them because you saw that the answer would be negative if you didn't? Is this something you just have to spot earlier on or is there a particular way to tell. Does it have something to do with the explanation on this page in the blue boxes?:

http://tutorial.math.lamar.edu/Class.../ParaArea.aspx

**PhyM23**)I do yes. So did you flip them because you saw that the answer would be negative if you didn't? Is this something you just have to spot earlier on or is there a particular way to tell. Does it have something to do with the explanation on this page in the blue boxes?:

http://tutorial.math.lamar.edu/Class.../ParaArea.aspx

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(Original post by

The answer will be the same whether you flip them or not ... It is done for convenience

**TeeEm**)The answer will be the same whether you flip them or not ... It is done for convenience

Please may you clarify why you mentioned in your solutions the direction of the curve? I.e. what significance does drawing arrows on the curve have?

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#16

(Original post by

Ah okay that's understandable.

Please may you clarify why you mentioned in your solutions the direction of the curve? I.e. what significance does drawing arrows on the curve have?

**PhyM23**)Ah okay that's understandable.

Please may you clarify why you mentioned in your solutions the direction of the curve? I.e. what significance does drawing arrows on the curve have?

No major significance but it shows how theta changes

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(Original post by

A curve in parametric has direction, which you get as the parameter increases.

No major significance but it shows how theta changes

**TeeEm**)A curve in parametric has direction, which you get as the parameter increases.

No major significance but it shows how theta changes

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#18

(Original post by

Ah okay. Why does the integral given as the answer only work out the area of the top part of the curve and not the bottom half of it as well?

**PhyM23**)Ah okay. Why does the integral given as the answer only work out the area of the top part of the curve and not the bottom half of it as well?

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(Original post by

because these limits are associated with the top half

**TeeEm**)because these limits are associated with the top half

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#20

(Original post by

But isn't the bottom half also between these two limits?

**PhyM23**)But isn't the bottom half also between these two limits?

from 2pi/3 to 5pi/3

or

-4pi/3 to -pi/3

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