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Unsure where the negative sign comes from -- integration

From the edexcel pure year 2 book, I'm unsure where the negative sign comes from, I understand everything else in the question:

They are working out the area of A1 why's there a negative sign in front of the entire thing on it all, final answer is the same as the one in the book:

my final answer ends up being :

0.25 * (2e^(-1) - 1)
instead of
0.25 * (1 - 2e^(-1))

Reply 1

0le

The second last step is probably where you messed up, but since you don't show your working out, we can't really say for sure.

Reply 2

anonymous230

sorry heres my working out hope its clear enough to read, the part above is just defining u=x du/dx = 1 , the same as the one in the solution book, everythings the same but i dont get the negative sign on the 2nd and 3rd last lines of the solution

Reply 3

0le

So yes, it is the second last step. You should break it down into more steps. Where you've substituted zero and -1/2 into the already integrated equation, do this step n several parts.

Essentially you are meant to get +1/4 instead of -1/4 because the bit in square brackets, when substituting zero, will give -1/4 and there will still be a negative sign outside the square brackets.

(edited 4 years ago)

Reply 4

anonymous230

Original post by 0le

So yes, it is the second last step. You should break it down into more steps. Where you've substituted zero and -1/2 into the already integrated equation, do this step n several parts.

is it ? i got the exact same thing apart from the giant brackets around it all with a negative sign, which came from the 3rd last step, why is there a negative sign before the square brackets?

Reply 5

0le

Original post by anonymous230

is it ? i got the exact same thing apart from the giant brackets around it all with a negative sign, which came from the 3rd last step, why is there a negative sign before the square brackets?

I think it is related to the fact the region is underneath the curve:
http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-areas-2009-1.pdf

But will need someone else to confirm or suggest otherwise.

Reply 6

anonymous230

Original post by 0le

im honestly not sure it could be something ive forgotten thanks a lot for ur help n efforts

Reply 7

zetamcfc

Original post by anonymous230

im honestly not sure it could be something ive forgotten thanks a lot for ur help n efforts

You are trying to find an area. You can't have a negative area. You have evaluated the definite integral correctly, but that is not what the question is asking.

Spoiler

(edited 4 years ago)

Reply 8

anonymous230

Original post by zetamcfc

You are trying to find an area. You can't have a negative area. You have evaluated the definite integral correctly, but that is not what the question is asking.

Spoiler

AHHH thats what it is lol didnt even realise yeh ur right thanks lol