Question about a center of mass/integrals problem
Set up the integrals to find the center of mass of an equilateraly triangle with density ρ(x,y)=K√ (x²+y²), with sides of length two and the midpoint of one side is the origin.
Ok first question..I know that the limits on the x integral are from -1 to 1, but I am not sure what to put for y's limits. I am not sure if it would be 0 to 2-2x, 0 to 2+2x, or 2+2x to 2-2x, so I need some help with this please.
Also, I know that I need to set up the integral for mass first. But after this, in my book, sometimes integrals are set up for x bar and y bar, and then in other cases integrals are set up for M_y and M_x. So my question is, which two should I do in the case of a triangle? Does it even make a difference?
Thanks so much for your help!