Math 125, Autumn 2005
Final Examination
1
8. (10 points) Find the x-coordinate of the centroid of the shaded region below.
(3,1)
2
2
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Math 125, Autumn 2006
Final Examination
1
1
9. (10 total points) Consider the region bounded by x = 1, x = 10, y = , and y = .
x
2x
(a) (8 points) Find the centroid of this region.
(b) (2 points) Determine whether the centroid lies inside the region.
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Math 125, Autumn, 2009
Final Examination
Page 8 of 10
9. (10 total points) Consider the region R bounded between the curves y = 5 − x2 and y = 4x2 .
(a) (3 points) Find the area of R.
(b) (3 points) Find the x-coordinate x of the centroid (center of mass) of R.
(c) (4 points) Find the y-coordinate y of the centroid (center of mass) of R.
Math 125, Spring 2006
Final Examination
9. (8 points) Find the x-coordinate x̄ of the center of mass of the region below.
y
(0,2)
(2,2)
(1,0)
x
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Math 125, Winter 2006
Final Examination
Page 9 of 11
9. (8 points) Consider the region bounded by the curves
y = x3 ,
x + y = 2,
√
y = − x.
The area of this region is 49/12. Find the x-coordinate of its center of mass. Leave your answer in
exact form: do not use decimal expansions.
y
(1,1)
x
(4, −2)