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?

Question

Please show all work

Answer 1

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