Dear Students,

I misspoke at the end of tonight's review session and I want to correct the record. The work to pump the gas out the tank turned out to be the integral from -10 to 10 of

(rho)(g)(10-y)(10-y^2) dy

The question arose whether that could be replaced by twice the integral from 0 to 10 and I said yes, because the function is even.

Except it's not even, so you can't make that simplification. This ought to make some sense (that it's not even): the work needed to move the very top slice of gas is small because it's close to the top. But the work needed to move the very bottom slice is large because it's got a long way to go. If the integrand were even, these bits of work to move pieces which are the same distance from the origin would be the same.

Formally, you can mutiply the integrand out as a polynomial and see that it's not an even function.

I apologize for the confusion.

Some have asked about office hours tomorrow, and there is at least one. Check the web site on the Examinations page near the stuff about the final. At least one CA is volunteering his time in Lowell Dining Hall tomorrow night, but go easy on them because the CA's of course have their own finals to study for!

You can also e-mail questions to your section leader or to me. I will answer any e-mail sent before 10pm tomorrow night.

Yours,
Matthew Leingang