Unless you live in Chicago, the new Problem of the Week may be unsettling because it is rife with bears. Not the cute kind of bears that get stuck in a rabbit's tree house because they may or may not be morbidly obese. ("Oh, bother.") No. These are the "I'd rather eat you, bones and all, than pretend that I am a cloud to hustle some bees out of their honey" kind of bears. The dangerous kind.
Are you thinking, "This must be an optimization problem, where you are asked to calculate the bear minimum"? If you did think that, please know that I am, as you read this sentence, smiling approvingly and giving you polite golf applause for your clever pun. However, this problem is all about definite integrals, so there is no time for joking around.
Steel yourself for the battle of your life! Attack this problem with your bear hands! But please, before you do, I would like the polite golf applause reciprocated.
Are you pro-derivatives? If so, well, our politics may clash in the new Problem of the Week, as it is firmly anti-derivative. Only one tool is allowed to solve this pair of problems--the power rule for integration. No u-substitution allowed!
The last Problem of the Week for 2011 is now posted, and it's feeling all festive. Take a journey deep into the cold, barren wastelands of the Northern ice cap and search among the iceburgs to find a certain toymaker's workshop. (In case you need help calculating the derivative of a polar equation.)
With a nod of his head and a wink of his eye, he will promptly ask you to stop trespassing, and for Christmas this year? A restraining order from Santa.
No, this is not how you planned things at all...