y= x^2/3  2/x^1/3 + 1 point A (8,4) lies on this curve and the curve crosses the xaxis at (1,0) the point B is (4,0) The line passes through AB. Find the equation of the line which I got to be y=x4 The finite region R is bounded by C, AB and the positive X axis . Find the area of R. I intergrated the line curve which I got to be 1/2x^2 4x3/5x^5/3+3x^2/3x I intergrated using the points 8 ad 1 which I think is wrong. Any ideas?? the answer is supposed to be 43/5.

SophieL1996
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 02042013 18:16

ghostwalker
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 02042013 18:30
(Original post by SophieL1996)
...
The curve is above the line, so you'd want "curve"  "line".
With that correction, you'd get the whole shaded area.
But you only want the crosshatched area, so you need to subtract the area in red only.
Alternatively, you could work out the area from x=1 to x=4 above the xaxis, and then add on the difference between the curve and the line between x=4 and x=8.
Motto: Do a sketch. 
davros
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 02042013 18:33
(Original post by SophieL1996)
y= x^2/3  2/x^1/3 + 1 point A (8,4) lies on this curve and the curve crosses the xaxis at (1,0) the point B is (4,0) The line passes through AB. Find the equation of the line which I got to be y=x4 The finite region R is bounded by C, AB and the positive X axis . Find the area of R. I intergrated the line curve which I got to be 1/2x^2 4x3/5x^5/3+3x^2/3x I intergrated using the points 8 ad 1 which I think is wrong. Any ideas?? the answer is supposed to be 43/5.
Is it supposed to be
or something different?
Does the question say the line passes through AB or the line passes through A and B or something else? I'm not sure how the positive xaxis comes in if you just need the area between C and the lineLast edited by davros; 02042013 at 18:35. Reason: ghostwalker's diagram helps! 
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 02042013 18:50
(Original post by ghostwalker)
Refering to the attached diagram.
The curve is above the line, so you'd want "curve"  "line".
With that correction, you'd get the whole shaded area.
But you only want the crosshatched area, so you need to subtract the area in red only.
Alternatively, you could work out the area from x=1 to x=4 above the xaxis, and then add on the difference between the curve and the line between x=4 and x=8.
Motto: Do a sketch. 
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 03042013 13:36
(Original post by davros)
Excellent diagram. I have used it to confirm the answer is indeed 43/5  let's hope the OP can get it too 
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 03042013 13:37
y= x^2/3  2/x^1/3 + 1 point A (8,4) lies on this curve and the curve crosses the xaxis at (1,0) the point B is (4,0) The line passes through AB. Find the equation of the line which I got to be y=x4 The finite region R is bounded by C, AB and the positive X axis . Find the area of R. I intergrated the line curve which I got to be 1/2x^2 4x3/5x^5/3+3x^2/3x I intergrated using the points 8 ad 1 which I think is wrong. Any ideas?? the answer is supposed to be 43/5.

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 03042013 13:44
(Original post by ghostwalker)
Refering to the attached diagram.
The curve is above the line, so you'd want "curve"  "line".
With that correction, you'd get the whole shaded area.
But you only want the crosshatched area, so you need to subtract the area in red only.
Alternatively, you could work out the area from x=1 to x=4 above the xaxis, and then add on the difference between the curve and the line between x=4 and x=8.
Motto: Do a sketch. 
Indeterminate
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 03042013 14:11
(Original post by SophieL1996)
y= x^2/3  2/x^1/3 + 1 point A (8,4) lies on this curve and the curve crosses the xaxis at (1,0) the point B is (4,0) The line passes through AB. Find the equation of the line which I got to be y=x4 The finite region R is bounded by C, AB and the positive X axis . Find the area of R. I intergrated the line curve which I got to be 1/2x^2 4x3/5x^5/3+3x^2/3x I intergrated using the points 8 ad 1 which I think is wrong. Any ideas?? the answer is supposed to be 43/5.
Note:
 asymptotes
 points where it crosses the axes.
 behaviour when x is small
 behaviour when x is large
They will not give you such a horrible question without a sketch in the exam. 
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 03042013 14:17
(Original post by Indeterminate)
I'm assuming they haven't given you a sketch. So, to aid your understanding, you could sketch the curve C using it's key features, with the line on the same set of axes.
Note:
 asymptotes
 points where it crosses the axes.
 behaviour when x is small
 behaviour when x is large
They will not give you such a horrible question without a sketch in the exam. 
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 03042013 14:20
(Original post by SophieL1996)
y= x^2/3  2/x^1/3 + 1 point A (8,4) lies on this curve and the curve crosses the xaxis at (1,0) the point B is (4,0) The line passes through AB. Find the equation of the line which I got to be y=x4 The finite region R is bounded by C, AB and the positive X axis . Find the area of R. I intergrated the line curve which I got to be 1/2x^2 4x3/5x^5/3+3x^2/3x I intergrated using the points 8 ad 1 which I think is wrong. Any ideas?? the answer is supposed to be 43/5.
and subtract the area under the line (from 4 to 8 triangle) from this

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 03042013 14:22
(Original post by SophieL1996)
sorry I am still confused... could you show me some of your working to get me started please? and in the diagram shouldn't the curve be a parabola ?
I tackled this the same as the last question you posted  in other words I integrated from x=1 to x=8 to get the total area under the curve for that range and then subtracted the area of the triangle with vertices at (4,0), (8,0) and (8,4), i.e. the triangle formed by the xaxis and the lines y=x4 and x=8.
What do you get when you integrate with respect to x?
(Original post by SophieL1996)
Thankyou for the diagram it explains a lot How come the area under the curve from 0 to 1 is not included in the shaded area ?Last edited by davros; 03042013 at 14:22. Reason: bad latex! 
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 03042013 14:25
(Original post by SophieL1996)
y= x^2/3  2/x^1/3 + 1 point A (8,4) lies on this curve and the curve crosses the xaxis at (1,0) the point B is (4,0) The line passes through AB. Find the equation of the line which I got to be y=x4 The finite region R is bounded by C, AB and the positive X axis . Find the area of R. I intergrated the line curve which I got to be 1/2x^2 4x3/5x^5/3+3x^2/3x I intergrated using the points 8 ad 1 which I think is wrong. Any ideas?? the answer is supposed to be 43/5.Last edited by davros; 03042013 at 14:27. 
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 03042013 17:49
Thanks everyone I got the correct answer!

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 03042013 18:08
(Original post by SophieL1996)
Thanks everyone I got the correct answer!
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