coorrdinates of centroid of region bounded by y-axis, y=x,

[alex83]

Let R be the region in the plane bounded by the y-axis , y=x, and y= 2/(x^2 + 1)

determine the coorrdinates of the centroid of R ??

i did draw the graph but (dont know how to post it )

any help on how i can start with this problem pls.

 

[stapel]

Duplicate post.

What formula(s) or algorithm(s) have they given you for this process? How far have you gotten in computing the moments?

Please be complete. Thank you!

 

[galactus]

Start by finding the area of the said region.

\(\displaystyle \text{Area=}\int_{0}^{1}\int_{x}^{\frac{2}{x^{2}+1}}dydx\)

Then, \(\displaystyle \overline{x}=\frac{1}{\text{Area}}\int\int x \;\ dA\)

\(\displaystyle \overline{y}=\frac{1}{\text{Area}}\int\int y \;\ dA\)

The graph shows the region you must find the centroid of.

 

[alex83]

thanks but if i have the area and want to avoid the double integrals how do i solve ??
\

the formula and method that our professor use is (MOMENTS )
where first he finds -lenght (which i cant fiqure out here )
- width which is dx here (i believe so )
-area which i already got and = (PI-1)/2
- mass or dm which is = delta * area

then Mx = integral y^~ dm
My = integral x^~ dm
M = integral dm

last
x= my/m
y=mx/m

this is the method we use in class but i couldnt plug it in this problem

thnx

 

[alex83]

thanks for ur reply

but i was trying this before i checked ur answer would u check it pls

first i set both equations equal to each other and got : x^3+x-2=0 ; solve it and got x=1

the question is i found these formulas in the book and want to set them up

Mx= 1/2 integral [a-b] g^2(x) - f^2(x) dx
My = integral [a-b] x(g(x)-f(x)) dx
M=integral [a-b] g(x)-f(x)

then set X=My/M and Y=Mx/M

is it right to use these in this problem ??
what should the integral limits[a-b] be ?? should it be [0-1]??/