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C2 intergration edexcel

SophieL1996

The diagram shows the finite region, R, bounded by the curve with equation y=x4+x), the line with equation y=12 and the y-axis. A) find coordinate A B) Find area R I have the coordinate as (2,12). I am having trouble with how to find the area. Any ideas?

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Reply 1

Jackabc

Original post by SophieL1996

Have you tried drawing a sketch?

Reply 2

Mr M

Study Forum Helper

Original post by SophieL1996

What is the equation?

Reply 3

SophieL1996

Original post by Mr M

What is the equation?

The equation for the curve is x(4+x) and for the line y=12

Reply 4

spanish_sahara

As it's quadratic there will be two answers, of which -6 is the other. You may find it easier with two coordinates. If I remember correctly, I think then you integrate and sub the x values in and subtract them from each other. Hope this helps, sorry my memory isn't too good but c2 was last year for me!

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Reply 5

Mr M

Study Forum Helper

Original post by SophieL1996

The equation for the curve is x(4+x) and for the line y=12

Ok that isn't what you put in your opening post!

Either change the subject and integrate

\int x \, dy

or find

\int y \, dx

and subtract your answer from the area of a rectangle.

Reply 6

SophieL1996

Sorry that is no help to me... The parabola is positive with the horizontal line through it, the area is between A (point of intersection) the y axis and (0,0) What do I take away from what ?

Reply 7

Mr M

Study Forum Helper

Original post by SophieL1996

Sorry that is no help to me... The parabola is positive with the horizontal line through it, the area is between A (point of intersection) the y axis and (0,0) What do I take away from what ?

Who are you talking to?

Do you want to integrate with respect to x or to y. Either will work so you choose?

Edit: As this is C2 I would strongly recommend x.

(edited 11 years ago)

Reply 8

Jackabc

Original post by SophieL1996

Sorry that is no help to me... The parabola is positive with the horizontal line through it, the area is between A (point of intersection) the y axis and (0,0) What do I take away from what ?

You can split it up into three rectangles, can you work it out from that?

Reply 9

SophieL1996

Original post by Jackabc

You can split it up into three rectangles, can you work it out from that?

No, as I have never been taught that

Reply 10

jadecross

Original post by SophieL1996

could you attach the diagram, it will make it easier for me to help :smile:

(edited 11 years ago)

Reply 11

SophieL1996

Original post by jadecross

could you attach the diagram, it will make this easier to help :smile:

Yes I have been trying to but it won't upload :frown:

Reply 12

Mr M

Study Forum Helper

Original post by SophieL1996

No, as I have never been taught that

Me neither.

:confused:

Reply 13

SophieL1996

so intergrate between 0 and 2 for equation of curve and minus that from (2x12) ??

Reply 14

Mr M

Study Forum Helper

The shaded area in this diagram is

\int_0^2 x(4+x) \, dx

Can you see a rectangle that you could subtract this area from to find the area you are interested in?

Reply 15

jadecross

Original post by SophieL1996

so intergrate between 0 and 2 for equation of curve and minus that from (2x12) ??

yes, it's as simple as that.

Reply 16

SophieL1996

Original post by jadecross

yes, it's as simple as that.

ok thanks I shall have a go :smile:

Reply 17

SophieL1996

Thanks I got the right answer of 40/3 thanks for all your help, especially the diagram (helped a lot!) :smile:

Reply 18

Jackabc

Original post by Mr M

Me neither.

:confused:

Original post by SophieL1996

No, as I have never been taught that

Isn't it bounded by all these graphs twice? So if you worked out the area between -4 and 0, added it to the area under -6 and -4 and then added it to the area between 0 and 2. Or was you just on about one side?

Edit: lol you could still split it up into three rectangles though if you added the areas between 0 and 1, 1 and 1.5, and 1.5 and 2 but that might take a bit longer.