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Calculus 2

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Calculus work problem. John bought the following corner lot. Two sides are bounded by 2 roads the back is bounded by a stream that follows the curve y = -x^3 + 8. He wants to build a house in the center of the lot. Where will that be?

Please show all work

  • Calculus 2 -

    I would approach this as a centroid problem.

    first, find the area under the curve

    area=int y dx from x=0 to 2
    and you put in for y, -x^3+8

    centroid x= (INT x*y dx )/area

    centroid y= (INT y*y dx)/area
    where in both of these y=8-x^3

    and the center will be the x,y you get

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