FP2 Summer 2009 Q1 where am I going wrong here.

The picture shows Q1 2009 FP2 OCR.
The answer I have is that there are two potential sets of rectangles to measure and the size comes down to
$0.3(f(0.3)+f(0.6)+f(0.9)+f(1.2)+f(1.5))\\$

for one set of rectangles and

$0.3(f(0)+f(0.3)+f(0.6)+f(0.9)+f(1.2))\\$

for the other.
The answers come out as -1.33131 and -0.5185 respectively.

Since we are asked for an upper bound and lower bound, I am tempted to put -0.5185 as the Upper Bound and -1.3131 as the Lower bound.

The Mark scheme says that the areas should be given as positive and if you use negative answers you lose two marks, which I find surprising.

The report goes so far as to say "A substantial number of candidates lost early marks by giving negative answers".

Whilst I understand a mark scheme (especially for Qu 1) giving full marks for UB 1.3131 and LB 0.5185 should we lose marks for giving negative areas for this Question, especially if we give the correct UB and LB for those numbers.

What am I doing wrong here to get different answers to the Mark scheme?

What am I doing wrong here to get different answers to the Mark scheme?

...

Well since it asks for the area, it should be positive. However, if you were integrating it, you'd get a negative value.

Seems a mean markscheme, IMHO. A trick, rather than testing genuine understanding.

Well since it asks for the area, it should be positive. However, if you were integrating it, you'd get a negative value.

Seems a mean mark scheme, IMHO. A trick, rather than testing genuine understanding.

Since we are asked for an upper bound and lower bound, I am tempted to put -0.5185 as the Upper Bound and -1.3131 as the Lower bound.

Seems a mean markscheme, IMHO. A trick, rather than testing genuine understanding.

...

And also, if you do take it in the negative form, you get the upper and lower bound the wrong way round

So far as I can tell, in pure maths, an area is a number, however if the convention is to take areas using magnitude then I am happy to go along.

If I am working on bounds with two negative numbers from a function, -1.3 and -0.5 (say) then the UB is -0.5 and the LB is -1.3. Those answers, given that I was being so radical as to consider a negative area, are not the wrong way round are they?

They would be the wrong way round according to the mark scheme (and the right answer), because the upper bound should have the 1.313 figure. If they saw you put -0.5 as the upper bound, what would happen?

But I think you are over complicating. Its like I have a square on top of the x axis with area 4. If I move it under the x axis, it still has area 4. I mean, how can you have a square with -4 area? What would it look like in real life :P It might be possible, but thats outside my range of knowledge :P

Well, firstly this is pure maths and not mechanics, even if it were not pure maths, if we can have negative mass then negative area is not a problem.

Well, firstly this is pure maths and not mechanics, even if it were not pure maths, if we can have negative mass then negative area is not a problem.
Secondly, my last contribution concerned a general answer to a function that outputs two numbers at its bounds and in that case it would be perfectly legitimate to have -0.5 as an UB and -1.3 as a LB. I do realise that that is not the case in this question, I should have made my writing more simple to read. Obviously, the mark scheme is right but that does not mean it is not mean. :-)

Well I agree with that.
However, I don't see why an area can't be negative. After all, numbers can be negative, even mass can be negative and as you say, the answer to the integral would be negative.
My main gripe is the removal of two marks from a 5 mark question and in Q1, why on earth do an area under the x axis when you are not making some point about negative areas. At FP2 testing whether negative areas are appreciated is a perfectly legitimate question. Implying that the question is somehow testing this and then rejecting a sensible answer, (that shows real understanding of LB and UB (IMO) ) is, as you say, mean.

In semiconductors, you have to use the concept of holes in order to explain the hall effect. The mass of holes can come out to be negative. As I said, if I can have to deal with negative mass in order to get some answers in Physics, then it does not seem to revolutionary to think about negative area in the purely theoretical area of pure maths.

FP2 wouldn't want you to think so abstractly as to use negative area.

So in question 1 we have to make sure we are not so abstract as to think about a negative area but in Q2 we have to distinguish real numbers and by question nine deal with imaginary ones.

Consider yourself fortunate they stop at imaginary (complex) numbers.