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C2 Quick Integration Question: Watch

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    (Original post by Dylann)
    I've attached a diagram to hopefully make this a bit clearer.

    Others have incorrectly said to integrate using 8 and 1 - you can only integrate between x-values.

    So you need to find the x-values when y=8 and when y=1 and then integrate this. You should realise that you did this in part a). Now, if you look at my diagram you should see how you could split the graph into a rectangle and another area. Working out the area of the rectangle (which is in the shaded region) should be straightfoward, the vertical height is from 1 to 8.

    However you must be careful, because when you integrated you calculated the area under the curve to the x-axis, and the shaded region does not include the x-axis. So you need to work out this area (straightforward) and take it away from the integrated area.

    Area of rectangle + area of integrated area (with the bit at the bottom taken away) = total area


    Ohhh, now it makes sense! Just one last question:

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    (Original post by creativebuzz)
    Ohhh, now it makes sense! Just one last question:

    Not quite - remember in part a) you integrated from "2" to "1"? Those are the limits of the area you are finding. So you only found the area from x=2 to x=1
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    (Original post by creativebuzz)
    Ohhh, now it makes sense! Just one last question:

    You integrated from 1 to 2 not the area under the entire curve


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    (Original post by Dylann)
    Not quite - remember in part a) you integrated from "2" to "1"? Those are the limits of the area you are finding. So you only found the area from x=2 to x=1
    Ah thank you, it all makes sense now! Positive rating given for such a brilliant explanation!
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    Was this not obvious from post 9,10 and 13? You only needed to see why the shape at the bottom of your area was a rectangle.

    (Original post by creativebuzz)
    Ah thank you, it all makes sense now! Positive rating given for such a brilliant explanation!
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    (Original post by WishingChaff)
    Was this not obvious from post 9,10 and 13? You only needed to see why the shape at the bottom of your area was a rectangle.
    I wouldn't mind helping OP for 60 whole pages, as long as they understand how to get the answer at the end. That's the most important part.

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