What should be an extremely simple question for some reason is frustrating me with answers that don't seem to make sense in my mind, and I've lost the sanity to ensure that my answer is correct.
As some quick rough estimates above, I calculated the area as simple rectangles in order to provide bounds on the possible answers that I would be expecting. That all said, my integration over the curve results in answers that are wildly outside my expected bounds. At this point I'm simply plugging the integral into a calculator and determining that I'm failing to properly set up my integral.
Side note: this is not a homework assignment, I'm estimating the required concrete I need for a tiny retaining wall (in cubic inches). Is there a seemingly visible error in the setup for the above integrals? Apologies if quick-fire questions like these aren't appropriate for mathexchange, bit of a hair-pulling day for a topic I thought I understood years back. If the problem lies in something beyond a typo, I'll fix up the question for future readers.