Tri 2 Week 6

This week was broken up by a snow day so it went by pretty fast. Even though we had the snow day we still managed to get in some quality learning. We started working on chapter 5 this week. 5.1 was about finite sums and using lram, mram, and rram to estimate areas under curves. Basically we just made rectangles and added up all of their sums. This was a pretty easy concept. Next in 5.2 we learned about definite integrals. In 5.2 all we really did was work on changing sigma notation into a definite integral. We also learned that when finding net area all the area above the x axis is positive and all the area below the x axis is negative. In 5.3 we learned about rules for integrals and the mean value theorem. The first rule was that the integral of f(x) on [a,b] is equal to the negative integral of f(x) on [b,a]. The second rule was the integral of f(x) on [a,a] equals zero. The third rule was that if you can factor out a number then you can put that number out front and multiply it back in at the end. There are three other rules but I don't really want to type them all out. They all make sense to me though. We learned about the mean value theorem on Friday and I still haven't fully grasped that but I also haven't done the homework for it yet so that is understandable. The mean value theorem says that there is a point a c on the interval [a,b] that will make the area. The function is 1/b-a times the integral of f(x) on the interval [a,b]. Again I don't fully understand this but I'm assuming that I will get it all figured out soon.