Hi all, I need some help on a couple questions:(adsbygoogle = window.adsbygoogle || []).push({});

1) Find the moment of inertia about the x-axis of a thin plate of constant density 1 (density = 1) bounded by the circle x^2 + y^2 = 4. Then use your result to find Iy and Io for the plate.

Here's how I was thinking to set it up:

Since the region R is a circle, I thought it would be best to take the double integral with order dy dx. So the limits of integration for x would be -2 < x < 2, and for y would be -sqrt(4-x^2) < y < sqrt(4-x^2), right? Since density = 1, wouldn't the setup for the double integral be this (sorry I don't know how to do an integral sign, so a "|" is supposed to represent that):

|| y^2 dy dx, with the limits of integration I said above

I did it this way and eventually I get to the point where I have to take the integral of (sqrt(4-x^2))^3 with respect to x. I haven't figured out how to do this, so I was just wondering if I'm on the right track or not.

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Next question:

2) Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y= x and y = 2 - x if density function = 6x + 3y + 3.

Once again I just want to check if I have set up this problem correctly. The limits of integration should be: 0 < y < 1, and y < x < 2-y ? And the order of integration should be dx dy ? So to find mass M of the plate I did this:

|| (6x + 3y + 3) dx dy, with the limits of integration as above

For My it would simply be: || x(6x+3y+3) dy dx, right?

Btw: all the inequalities should be <= instead of just <

Thanks

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# Moment of inertia and Center of mass questions

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