Greetings all, this is my first post on these forums.

I'm attempting to construct an inverted catenary that will intersect the x-axis at y=0 and y=1 and have an area of 1 bound by the x-axis and the function.

I started off with

and that satisfies the intersection points, but does not have an area of 1. So to get the area closer to one, I kept manipulating the numbers and integrating, until I came to

This gives an area of 1.0000 under the curve bound by the x-axis, but I'm sure it's not actually equalling 1, I've just reached the limit of my program's (winplot) decimal display.

My goal is to find a more systematic approach, since repeatedly adjusting the numbers isn't exact. I wonder if there could be some sort of series representation for the function. I don't recognize the number 1.543405 as anything special, but perhaps it could be respresented exactly, rather than a decimal (eg. to say pi rather than 3.141592) and yield the proper results.

Thanks in advance for any help!

Cheers.