CM of triangle with integration

AI Thread Summary
To calculate the center of mass of an isosceles triangle using integration, the density is constant. The formula for the center of mass involves double integrals of x and y coordinates divided by the total mass. The user initially struggled with defining the boundaries for integration, suggesting that x ranges from -c/2 to c/2. The boundary for y was clarified as simply being b, as the triangle can be viewed as composed of two right triangles. The user ultimately resolved their question regarding the integration limits.
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Homework Statement



I need to calculate center of mass of this isosceles triangle using integration:
42pw9.png

the density is constant.

Homework Equations


Rcm = integral(xdm) / integral(dm)

The Attempt at a Solution


I know how to begin:
dm = density * dx * dy;
x = double-integral(x*dx*dy) / integral(dy*dx);
y = double-integral(y*dx*dy) / integral(dy*dx);

I have problem with defining the boundaries of integration.
let's say that c is the base and b is the height of this triangle.
I think that -c/2 to c/2 are the boundaries for x, but I have no idea what the boundaries for y are. I know how to solve similar problem with right triangle, a boundary for y there is defined by function b-(b/a)x. Any help?
 
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The triangle is made of two right triangles.

ehild
 
Really?! OMG!
I see that myself. What I asked is integration limit. I've solved it myself already, the limit is simply b.
 

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