The Integral of TheTwelve Days of Christmas

Ok, so here's the background on this one:

The church play this year was about the origins of The 12 Days of Christmas. They sang a version using the things the song represents, i.e 11 faithful apostles instead of lords a leaping. Our family also has several other versions on tape and cd at home, 5 onion rings, a japanese transistor radio, a beer in a tree.. you get the idea. On the way home from the Rockettes, The 12 Days of Christmas was on the radio and we all started singing along but different versions, so Wendy said, "I wonder how many different versions you could fit in one song."

At first I suggested 12! (factorial) but soon realized this was wrong as that is multiplication. "There must be some term for adding everything instead of multiplying," I said to Wendy. Wendy pondered a bit, "Yeah, sigma." "Oh, yeah, summation!" I exclaimed, "Then we should be able to do an integral!" So Wendy and I brain-stormed and discussed and decided we wanted to use the interval from 1 to 12, being that there are 12 days in the song. So, we had to devise the correct equation for the line representing the song. We knew the slope had to be 1 as we were dealing with whole numbers and for each new verse goes up one (i.e. 2 calling birds to 3 french hens). So first we tried y=x from 1-12, that did not work, so we played around until we found the correct equation.

Ladies and gentleman the integral for The Twelve Days of Christmas is: The integral from 1 to 12 of x+2. S(x+2)dx from 1 - 12. And there are 71 total possible things to sing about!

(Then we just had to explain to Katrina what on earth we were doing!)

(Original Post)

Nerdy