Year 12s: what will be the first way you research your future options? >>

c4 parametric equations help!

confused

can anyone teach me how to find an appropriate limits?
for example, In question 7 below, the sample answer uses the t=1,0 when x=0, -1 as the limit. However, I got the same result when I uses only x=O and therefore t=1 and -1 as the limit of integral. is it just a coincidence or it is an alternative way to answer the question? If it is another method to answer the question, why? can you explain to me ? thank you very much!

Lamalam

Reply 1

the bear

if you put -1 for t in the integral you do not get 0 in the second bracket ?

Original post by the bear

if you put -1 for t in the integral you do not get 0 in the second bracket ?

When I sub x= -1 , the value of t is zero only , I cant proceed :-/

Posted from TSR Mobile

Reply 4

Lamalam

Original post by davros

You can't "use only x=0" - that doesn't make sense! Any integral where the 2 limits are the same would come out as 0 by definition.

Is there another way to solve this problem ?? :-/

Posted from TSR Mobile

Reply 5

TenOfThem

Original post by Lamalam

Is there another way to solve this problem ?? :-/

Posted from TSR Mobile

I am not really sure what your thinking is

You do, I assume, understand that if you try to do this as a single integral then it is bound to come out as zero because the section below the axis will cancel out the section above the axis

So you need to think about the curve between x=-1 and x=0, find either the positive section OR the negative section, and then double that

Clearly when x=-1, t=0 so that gives one of your limits

When x=0, t= 1 or -1 ... you need to realise that integrating between t=-1 and t=0 will give you one half of the space and that integrating between t=0 and t=-1 will give you the other half

So, you choose one of these pairs, integrate and double

You could do both of them - you will see that one is 4/15 (above the axis) and the other is -4/15 (below the axis)

Giving a total of 8/15 either way

Reply 6

davros

Original post by Lamalam

Is there another way to solve this problem ?? :-/

Posted from TSR Mobile

Yes, you need to integrate from the left-most intersection with the x-axis to the point (0,0) to get the area of the top loop and then use symmetry to get the area of the bottom of the loop.

You can't integrate from a point back to the same point - you'll always get 0 (well, at least in A level maths :smile: