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I've been working on this problem for a few days and I'm pretty stuck. I'm working on how much area is eclipsed by some arbitrary planet by another over a given time. My question is if I have two circles one given by (y-100)^2+x^2 = 100^2 and the other given by (y+100)^2+x^2 = 100^2, how much area will be between those two curves as the second circle is shifted up until it is directly on top of the other circle?

my attempt to do this was to make the first circle (y-100)^2+x^2 = 100^2 and the second circle (y+100-t)^2+x^2 = 100^2. I would then want to find the area between those two curves as t goes from 0 to 200.

My ability to take integrals with multiple variables is poor but I will be taking calc 3 next semester so that should help.

any information on how to set this up or general help would be greatly appreciated.

Thanks