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    The sketch shows part of the curve with equation y = x2(x + 4). The finite region R1 is bounded by the curve and the negative x axis. The finite region R2 is bounded by the curve, the positive x axis and the AB, where A(2,24) and B(b,0)

    The area of R1= The area of R2

    a - Find the area of R1
    b - Find the value of b I find the area which is 64/3. However I do not know how to find b.
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    (Original post by SophieL1996)
    The sketch shows part of the curve with equation y = x2(x + 4). The finite region R1 is bounded by the curve and the negative x axis. The finite region R2 is bounded by the curve, the positive x axis and the AB, where A(2,24) and B(b,0)

    The area of R1= The area of R2

    a - Find the area of R1
    b - Find the value of b I find the area which is 64/3. However I do not know how to find b.
    It's not known whether b<2 or b>2. What you can do is work out the area under the curve from 0 to 2. If this is less than 64/3 then b must lie to the right of x=2 so you can form a triangle PBA where P is (2,0), work out its area in terms of b and then set area under curve + triangle area = 64/3 to work out what b must be!
 
 
 
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