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. Find the center of mass of a thin flat plate bounded by the curve x = y^ 2 and the line x = 1 if the density at any point (x, y) is given by δ(y) = y + 1.

MYnameisJames said: i truly wish i knew. im guessing length times width times height? Click to expand... That would give you a volume. If we have a N masses at discrete points what we do is take a weighted average of the position (a literal weighted average in this case): $$\displaystyle y_{cm} = \dfrac{1}{M} \sum_{i = 1}^N m_i y_i$$ where M is the total mass. This is for one dimension. If you have masses at points in two dimensions then you need to do another one for the y component. To convert this to a continuous mass then you need to find the weighted average at each point using the density function, ie. $$\displaystyle y_{cm} = \dfrac{1}{M} \int \delta (y) y ~ dy$$ To find the total mass you simply calculate the same thing without the extra y: $$\displaystyle M= \int \delta (y) ~ dy$$ Give it a try and show us what you get. -Dan