SOLUTION: Find (x,y) position of the centroid of the area under the curve y=1+x+x^2.from x =1,x=2.?

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Question 911570: Find (x,y) position of the centroid of the area under the curve y=1+x+x^2.from x =1,x=2.?
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First integrate to find the area.

To find the centroid,
x=%281%2FA%29%2Aint%28x%5Be%5D%2CdA%2Cx=1%2Cx=2%29
and
y=%281%2FA%29%2Aint%28y%5Be%5D%2CdA%2Cx=1%2Cx=2%29
where x%5Be%5D and y%5Be%5D are the centroid of the differential element dA
x%5Be%5D=x
y%5Be%5D=y%2F2
So substituting,

and
x=%2891%2F12%29%2F%2829%2F6%29
x=91%2F58
.
.
.

and
y=%28247%2F20%29%2F%2829%2F6%29
y=741%2F290
.
.
.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
y = x^2 + x + 1
Take Integral
f(x) = x^3/3 + x^2/2 + x
A = f(2) - f(1) = 20/3 - 11/6 = 4.833
x = (1/A)
Evaluating: x^4/4 + x^3/3 + x^2/2] from 1 to 2 = 7.5833
y = (1/A)int%28%28+x%5E2+%2B+x+%2B+1%29%5E2%2F2%2C+dx%2C+1%2C+2%29