I have some good news, and then I have some bad news.
Good news: the second one’s done!!! Never again, right?!!!
Bad news: the average was 60%, hmm…..whatever.
It’s alright though, looking back, those problems seem tough. That’s why I took some of the hard ones out.
As homework, we’re not moving on, juuuust yet. We’re going to have those same ones be modified and as practice. The next set is practically the hard problems again. This week is over the hard ones.
Reason? If we kept going, the rest of the board for most of us would read:
adfadfadfdfadsfadfafdfadfasdfasdfadsfasd fasdfasdfasdfasdfasdfasdfasdfasdfasdfasdf adasdfasdfdsfasdfasdfasdfasdfasdfasdfasdfa fasdfsadfasdfasdfasdfasdfasdfasdfasdfasdf adfaadfasdfasdfasdfasdfsadfasdfasdfasdf dfasdfasdfadsfsdfasdfasdfasdfasdfasdfdsfas. okay, now go do that next set!!
See what I mean?
Common Mistake
The most common mistake this time around was not computing the double integral for the function $r = \sin(\theta)$ using the area method. Rather than have
\[\int_{0}^{\pi/2} \sin(\theta)d\theta\](this is for a cartesian coordinate system)
remember the form
\[\int_{\theta_1}^{\theta_2} \int_{0}^{r} rdrd\theta\]and the rest follows! Don’t worry, there’s more problems on them, so we’ll know them better.
Catch you next time! See me if you have any exam questions, better now than later. I’m available after class, office hours, and on a chat forum sometimes. If you’d like, we can meet by appointment.
(just an illustration.)