Calculus 2
posted by Laura .
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

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=8x^3
and the center will be the x,y you get