Small background: I am a mathematician student, currently my first year in university. This problem is a calculus problem. So I am meant to solve this using calculus.
My questions before presenting this problem is; How do I break down this problem? Where do I start? Do you have any tips on what I can do? What would you do when encountering this problem? What can I/others learn in the future doing problems like these?
An homogeneous plate ($\rho $) that lies on a table. The table has the coordinate system $\Omega \:=\:\lbrace a\le x\le b,\:0\le y\le f\left(x\right)\rbrace $, where $f\::\:\left[a,b\right]\:\Longrightarrow \:\mathbb{R}$ is a positive and continuous function.
We know that the center of mass for $\Omega $ is the point $\left(X,Y\right)$ <- (Those are vectors I guess).
If $P$ is a plate that is made by the same material as $\rho $, but extens over the area $\Omega P$, that is defined by $g\left(x\right)=\:\alpha \:f\left(x+\phi \right)$, where is the masscenter to $\rho $?
My first intuition is to find the domain of $P$, but I'm not sure how to do this, and even solve this.
Any help/hints/tips is appreciated!
Thank you very much that this math forum exists : - )