posted by .

Find the centroid of the area bounded by the parabola y=4-x^2 and the x-axis

A.(0,1.6)
B.(0,1.7)
C.(0,1.8)
D.(0,1.9)

domain from -2 to +2 but due to symmetry just do from 0 to 2

Area = int y dx = 4 x-x^3/3 from 0 to 2
= 8 -8/3 = 16/3

moment = (1/2)int y^2 dx
= (1/2) int[ 16-8x^2+x^4]
= (1/2) [ 16 x - 8 x^3/3 + x^5/5] 0 to 2
= (1/2)[32 -64/3 +32/5]
= 8.5333

moment/area = 8.5333*3/16

= 1.6

In general, finding the centroid of a curved region can be a very messy question.
See this pdf page, with 2 examples at the beginning
http://pages.pacificcoast.net/~cazelais/187/centroids.pdf

Because of the symmetry of your equation, we know that the centroid has to be on the y-axis, as seen by your choices of answers.
It must be up the y-axis in such a way that the area above must be equal to the area below, or 1/2 the total area

total area = 2∫(4-x^2 ) dx from 0 to 2
= 2[ 4x - x^3/3] from 0 to 2
= 2[ 8 - 8/3 - 0] = 32/3

so 1/2 the area is 16/3

taking horizontal slices from y to 4
area = ∫(4-y)^.5 dy from y to 4
= [ (-2/3)(4-y)^(3/2) ] from y to 4
= [ (-2/3)(0)^(3/2) - (-2/3)(4-y)^(3/2) ] = 8/3 only considering the area in 1st quadrant

(2/3)(4-y)^(3/2) = 8/3
(4-y)^3/2 = 4
4 - y = 4^(2/3) = 2.5198
y = 1.48

ARGGG! , none of your choices, check my arithmetic

another senior moment for me.

Similar Questions

1. calculus

could some body please check this for me?
2. Calculus (double check )

Find the centroid of the area bonded by the parabola y =4-x^2 and the x-axis?
3. calculus

Find the area of the region bounded by the parabola y=x^2 , the tangent line to this parabola at (10, 100), and the x-axis.
4. Calculus

Find the centroid of the area bounded by the parabola y = 4 - x^2 and the x-axis. A. (0,1.6) B. (0,1.7) C. (0,1.8) D. (0,1.9) Find the average value of the function i=15(1-3^-1/2t) from t=0 to t=4. A. 7.5(1+e^-2) B. 7.5(2+e^-2) C. …
5. calculus

Find the coordinates of the centroid of the following volume of revolution formed by rotating the area bounded by y^2-4=-x^2, x=0,x=1, And the "x" axis about the "x" axis.
6. Parabola Ques

Find the point P on the parabola y^2 = 4ax such that area bounded by parabola, the X-axis and the tangent at P is equal to that of bounded by the parabola, the X-axis and the normal at P.
7. calculus 2

Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.
8. calculus 2

Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.
9. Calculus: Centers of Mass

Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y^2 = 2x, and the line x + y = 4. I've graphed the function, and it looks like a triangle with one side curved (the parabola). I'm not quite …
10. calculs

Find the point of the parabola z= x^2+y^2 which is closest to the point (3 -6 4) B_ find the centroid of the first quare the area bounded by parabola y=x^2 and the line y= x2bar Cadet ermine the centroid of the first quarter to area …

More Similar Questions