This week was more slope fields, integrals and antidifferentiation. We integrated with and without U substitution. We integrated using x and y seperating the variables. The week was cut short by a snowday on Friday, but we had a test on Thursday that we were supposed to finish on Friday. I hope I didnt forget all of the material over the three day weekend. It is very possible that I did, but I am holding out hope. It is possible that we will have another snowday or two next week as the low temperature on Thursday is -13 and we are supposed to get three inches of snow on Monday. Who knows. This picture perfectly embodies how it feels to live in Michigan this winter.

This week in Calc, we did more integrals, and we were introduced to the idea of slope fields. Slope fields give you a good way to visualize a function from its antiderivative. They can also help you figure out integrals that would otherwise be impossible. We took a quiz on the same topic. I think I did fairly well on it. I finished pretty quickly although I couldn't for the life of me remember that the antiderivative of lnx is 1/x. I probably will not forget that anymore. Other than that I think the quiz went well. We then worked on differentiating for x and y. That led to a conversation about the use of c and k both for arbitrary constants. To illustrate that it doesn't matter what variables one uses, I did algebra with smiley faces to prove my point.

This week we worked on antidifferentiation. It honestly felt really cool to work on some of the long complicated problems. You'll work for a while not see anything, and then all the sudden you see some trick or some trigonometric identity that unlocks the rest of the problem and then you're done! It's oddly exciting for a math problem. It feels very fulfilling once you finish. I feel like didn't learn the material on U substitution for definite integrals. I'll have to look at that part of the chapter more in depth. Although there really aren't that many examples of that kind of problem in the book, maybe I'll ask you for help. I'll leave you with a picture of a fun problem we did the other day.