# Calculus - Center of Mass

Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2.

X = 1/Area*Integral from a to b: x*f(x)dx
Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx

How do I find the area for this? Once I know that, is this the correct set up?

X = 1/Area*Integral from 1 to 2: [x*(1/x)]dx
X = 1/Area*[x] evaluated at 1 and 2

Y = 1/Area*Integral from 1 to 2:
[(1/2)*(1/x)^2]dx
Y = 1/Area*[(-1/x] evaluated at 1 and 2.

Thanks.

area= INT y dx =INT dx/x= ln x from 1,2

yES, Those are the correct equations for the first moment.

Ok, thanks for checking and for helping.

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### math

find the exact coordinates of the point on a circle of radius 5 at an angle of 5pi/3. thanks for any help! (:

2. ### calculus

Find the centroid (¯ x, ¯ y) of the region bounded by: y = 6x^2+7x, y = 0, x = 0, and x = 7

3. ### Need Help Please- Pre-Calc

The coordinates of the five quarter points for y=sin(x) are given below. Use these quarter points to determine the​ y-coordinates of the quarter points of y=5sin(-π/3x). (0,0) (π/2,1) (π,0) (3π/2,-1) (2π,0) (Type ordered

4. ### calculus

find the centroid of the area betwen the curves 2y=x^2; y= x^3

1. ### calculus

find the coordinates of the centroid bounded by y=25x^2 and y=4. the region is covered by a thin flat plate

2. ### math

You start a search for a buried object by marking the center of a field as (0, 0), with coordinates giving distances in yards. Coordinates to the north or east are positive, and coordinates to the south or west are negative. You

1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

4. ### maths

The rectangular coordinates of a point are given (-5,-5root3). Find polar coordinates of the point. Express theta in radians. Answer must be in form ​(Type an ordered pair. Type an exact answer in terms of pi.Use integers or

1. ### math

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down. A)Write the coordinated of the vertices of the image after reflection. B)Write a rule for the translation. Use arrow rotation.

2. ### geometry

Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the coordinates of the centroid. Find the coordinates of the circumcenter. Find the coordinates of the orthocenter. Find the equation of the line.

3. ### Calculus

Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9. -------------- Is this basically 1/4 of an oval/ellipse? If so then the area would be: pi*9*3, correct? So the X coordinate would equal: 1/Area * Integral from

4. ### calculus 2

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, y