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    The curve has the equation y=x^2+1 and the line has equation y=7-x. The finite region, R1, is bounded by the line and the curve. The finite region, R2, is below the curve and the line and is bounded by the positive x and y axes.

    a) Find R1
    b) Find R2

    What I did is different to the solution given. I found R1 and R2 intersect at (-3,10) and (2,5). I used the limits 2 and -3 to find the area under the curve. Then to find the total area, I saw you could form a trapezium. I found the area of the trapezium and subtracted it from the area under the curve to find R1. Can someone tell me why that is wrong please?

    The other way I just found out is to just subtract the area under y=7-x and y=x^2+1. This gets you the correct answer however I'm still not sure why my method 1st time was wrong?
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    (Original post by dont know it)
    The curve has the equation y=x^2+1 and the line has equation y=7-x. The finite region, R1, is bounded by the line and the curve. The finite region, R2, is below the curve and the line and is bounded by the positive x and y axes.

    a) Find R1
    b) Find R2

    What I did is different to the solution given. I found R1 and R2 intersect at (-3,10) and (2,5). I used the limits 2 and -3 to find the area under the curve. Then to find the total area, I saw you could form a trapezium. I found the area of the trapezium and subtracted it from the area under the curve to find R1. Can someone tell me why that is wrong please?

    The other way I just found out is to just subtract the area under y=7-x and y=x^2+1. This gets you the correct answer however I'm still not sure why my method 1st time was wrong?
    Although I am terrible at shapes and geometry, I am struggling to see the trapezium.

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    (Original post by dont know it)
    The curve has the equation y=x^2+1 and the line has equation y=7-x. The finite region, R1, is bounded by the line and the curve. The finite region, R2, is below the curve and the line and is bounded by the positive x and y axes.

    a) Find R1
    b) Find R2

    What I did is different to the solution given. I found R1 and R2 intersect at (-3,10) and (2,5). I used the limits 2 and -3 to find the area under the curve. Then to find the total area, I saw you could form a trapezium. I found the area of the trapezium and subtracted it from the area under the curve to find R1. Can someone tell me why that is wrong please?

    The other way I just found out is to just subtract the area under y=7-x and y=x^2+1. This gets you the correct answer however I'm still not sure why my method 1st time was wrong?
    Area under curve = 50/3

    Area of trapezium = 1/2 (10+5)*5 = 75/2

    Area in between = 75/2 - 50/3 = 125/6 which is correct.

    You need to show us your calculation for us to determine what went wrong.
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    You may have tripped up in the areas or integration or some sort of calculator mistake.
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    (Original post by Kevin De Bruyne)
    Although I am terrible at shapes and geometry, I am struggling to see the trapezium.

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    Not sure if my sarcasm detector is broken, but:

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    (Original post by dont know it)
    The other way I just found out is to just subtract the area under y=7-x
    Note that the area underneath a straight line y = mx + c between the points (a,ma+c) and (b,mb+c) is precisely a trapezium:

    \displaystyle

\begin{align*} \int_{a}^b mx+c\,\mathrm{d}x &= \frac{mx^2}{2} + cx]_{a}^b  \\ & = \frac{mb^2}{2} + cb - \frac{ma^2}{2} - ca \\ & = \frac{m}{2}(b-a)(b+a) + c(b-a) \\& = \frac{b-a}{2}(m(b+a) + 2c) \\& = \frac{1}{2}(b-a)(ma+c + mb+c)\end{align*}
 
 
 
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