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# Integration

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1. Just doing a past paper from June 2006 C2

https://c4a3f001dcd45afe69d0ceec8300...%20Edexcel.pdf

Question 10

I got the equation of the line AN y=-12x+40

So I done took the equation of the line away from the equation of the curve to get

x^3 - 8x^2 + 32x - 40

I then integrated this to get

1/4x^4 - 8/3x^3 +16x^2 - 40x

with the limits 10/3 and 0

BUT I cant seem to get the right answer using this method :-(

Can someone just show me where I have gone wrong coz I think Ive gone blind to any mistakes now....

I know that there are two ways of doing it - finding the area of the triangle which ive done etc. But just outta curiosity I tried this way and no matter what I DO I cant get the same answer....
2. (Original post by christinajane)
Just doing a past paper from June 2006 C2

https://c4a3f001dcd45afe69d0ceec8300...%20Edexcel.pdf

Question 10

I got the equation of the line AN y=-12x+40

So I done took the equation of the line away from the equation of the curve to get

x^3 - 8x^2 + 32x - 40

I then integrated this to get

1/4x^4 - 8/3x^3 +16x^2 - 40x

with the limits 10/3 and 0

BUT I cant seem to get the right answer using this method :-(

Can someone just show me where I have gone wrong coz I think Ive gone blind to any mistakes now....

I know that there are two ways of doing it - finding the area of the triangle which ive done etc. But just outta curiosity I tried this way and no matter what I DO I cant get the same answer....
The method you are using is to find the "area enclosed by a curve and a line".

This region is enclosed by the curve, the line and the x-axis. It is not only enclosed by the curve and the line.

So the method would not work here.
3. (Original post by notnek)
The method you are using is to find the "area enclosed by a curve and a line".

This region is enclosed by the curve, the line and the x-axis. It is not only enclosed by the curve and the line.

So the method would not work here.
Oh - I guess I thought I took the x axis into account because of the limits, 10/3 and 0

So for future reference if it involves the x axis dont use this method? Just want to pick the right one in an exam!
4. (Original post by christinajane)
Oh - I guess I thought I took the x axis into account because of the limits, 10/3 and 0

So for future reference if it involves the x axis dont use this method? Just want to pick the right one in an exam!
I'm confused, i thought this method included the x axis, let me work through the question
5. (Original post by LewisClothier)
I'm confused, i thought this method included the x axis, let me work through the question
Yeah I am still a bit - I thought it did too - unless ive calculated something else wrong....
6. (Original post by christinajane)
Oh - I guess I thought I took the x axis into account because of the limits, 10/3 and 0

So for future reference if it involves the x axis dont use this method? Just want to pick the right one in an exam!
did you just integrate under the curve? or did you integrate with the line - the curve?

when you have two lines or a curve and a line you need to take the one that is underneath away from the one on top then integrate, It's difficult to explain
7. (Original post by LewisClothier)
did you just integrate under the curve? or did you integrate with the line - the curve?

when you have two lines or a curve and a line you need to take the one that is underneath away from the one on top then integrate, It's difficult to explain
I done the curve minus the line, because the curve was over the line and then integrated the resulting equation...
8. (Original post by christinajane)
Yeah I am still a bit - I thought it did too - unless ive calculated something else wrong....
yeah i just did it how i usually would and didn't get the answer on the mark scheme...
9. (Original post by LewisClothier)
yeah i just did it how i usually would and didn't get the answer on the mark scheme...
Yeah weird - Its driving me insane
10. (Original post by christinajane)
I done the curve minus the line, because the curve was over the line and then integrated the resulting equation...
pretty sure you have to do the line - the curve but it obviously just comes out the same but positive, i don't know here, sorry
11. (Original post by christinajane)
Yeah weird - Its driving me insane
did you get 1900/81 ?
12. Yeah no worries - maybe notnek is right but it seems to make sense what we did....

Because I have done the same thing in the past with other questions and its worked...
13. (Original post by LewisClothier)
did you get 1900/81 ?
Yeah it was something over 81 - not sure now coz i threw my paper in the bin in frustration.

Will have another go at it in a lil bit - will probably get something completely different now!
14. (Original post by christinajane)
Yeah it was something over 81 - not sure now coz i threw my paper in the bin in frustration.

Will have another go at it in a lil bit - will probably get something completely different now!
I can't even work out what they've done on the mark scheme, can you?
15. (Original post by christinajane)
Yeah it was something over 81 - not sure now coz i threw my paper in the bin in frustration.

Will have another go at it in a lil bit - will probably get something completely different now!
https://www.youtube.com/watch?v=CRTYcP80GdE
16. I dont even know how they decipher mark schemes in general!

But find the area of the triangle and then add that to the integrated bit between the limits of 0 and 2.

I know I should jsut stick with that one - but its just annoying me that this method - which should work, doesnt give the right answer.
17. (Original post by christinajane)
I dont even know how they decipher mark schemes in general!

But find the area of the triangle and then add that to the integrated bit between the limits of 0 and 2.

I know I should jsut stick with that one - but its just annoying me that this method - which should work, doesnt give the right answer.
The area that you have found is the blue area plus the green area (they will have opposite signs and cancel each other out a little).

As you can see, the area that you have found (the area between the curve and the line) is nothing close to the area that you need to find.
18. (Original post by christinajane)
Yeah weird - Its driving me insane
It won't work here as I said. Think about what

The method you are using is to find the "area enclosed by a curve and a line".

This region is enclosed by the curve, the line and the x-axis. It is not only enclosed by the curve and the line.

So the method would not work here.
Just adding to this, you can also use the method to find the area enclosed by two curves and two vertical lines and .
19. Why does the subtraction method work:

So what you're actually doing is subtracting the area under the red line from the area under the blue line. You should be able to see that this gives the green area.

Now in your question, what you have done is subtract the area under the line between 0 and N from the area under the curve between 0 and N. Look at your diagram and think about why that won't give you the required area.
20. Ahh ok

So when Ive used this method in the past its only been when the line interests the curve and doesnt involve the x axis - which you mentioned earlier.

Thats why Im getting them both a little muddled up.

Thanks to you all - that visual really helped me understand Zacken, as well.

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