A thin plate with constant mass per unit area has edges defind by the curves,
where a>0 is a constant. Find the first moment of the plate about the x-axis.
See figure attached for my attempt. I've draw a quick sketch in the top right of the page.
I'm first calculating the total mass of the plate, then I can find the first moment of the entire plate about the x-axis.
I'm going to first solve M.
Is there integral I've set up correct?
The one step I'm worried about is when I was left to integrate,
if I had done that one correctly.
Is there perhaps another route of integrations that I should proceed with? Can anyone spot any other errors?