I'm new here. If I break any rule, please, tell me and I will fix it immediately.
Well, long story short. Due to COVID-19, I had some financial troubles and I coudln't keep up paying my internet service for a couple of weeks. I'm currently studying Software Engineering and I missed a lot of Online classes with literally no way to get in touch with my teacher.
I had some assignments which, I've been struggling solving them, but gladly, I'm currently in the last assignment until now. I need to solve 50 exercises, but I really missed the base for solving them, If someone could help me out with the first one, I'll be incredibly thankful and I'm sure it'll help me out with the topic, here's the problem:
"Calculate moments about the X and Y-axis. Calculate the mass and center of mass. Consider $\rho = x + y$"
Functions: $g(x)=-x-10 / f(x)=-x^2+2x$
On the bottom says: Use fractions, don't leave blanks spaces between signs and numbers, for example, $-151/7$
My teacher just uploaded this example to the class feed, but he won't be able to support us. I can't really relate it to the kind of problems in the assignment...
This is the first assignment problem:
This is the example:
I may be mis-reading, but I don't think the question is set up correctly. Let's just look at the mass. The mass should be the double integral of the density over the given region:
$$m = \int_{-2}^5 \int_{-x-10}^{-x^2+2x} \rho \; dy \; dx.$$
Since $\rho$ is a function of $x$ and $y$, it needs to be inside the integral. And when you're done integrating, $\rho$ won't appear in the answer. But the blanks for the answers have $\rho$ next to them. This would be the format if $\rho$ were constant (that is, if you had uniform density.)
So it looks like your instructor set up the problem as if it were a uniform density problem, and then gave you a non-uniform density. You might gently ask him if he's attempted to answer the question himself.