his week is calculus we took the chapter 5 test and u substitution came back to haunt me in chapter 6. Overall I felt pretty good about the chapter 5 test. I have figured out that i have a pretty god understanding of integrals because chapter 5 is the first chapter this whole year that I fully understood what I was doing. Sadly, it was a short lived glory because now were learning how to do definite and indefinite integrals using U substitution. This has been very difficult for me because I did not understand how to use U substitution when we learned it the first time so I'm trying to figure that out along with do the integral part. When I was doing the assignment I started to semi understand how to do it but its still a struggle. I have figured out how to do it when u is very obviously given to me but if it is a trig identity or not clearly stated I get very confused. Even though I still dot completly undertsand U substitution I'm slowly learning it for example this week I released that du is the thing that can be canceled out which is one thing i did not pick on before. I'm hoping if i practice it more I will get way better at it.
When learning the fundamental theorem of calculus I primarily relied on deductive learning. I have always been a deductive learner because just knowing the definition of the theorem does not click for me. I need to see an example of how to apply this theorem before I will understand it. The fundamental theorem of Calculus is important because it combines derivatives with integrals and helps find the area for exact data points which is more useful than just being able to find the derivative. To me the fundamental theorem of calculus means that you can find the integral without a calculator by finding the antiderivative and subtracting F(B)-F(A). The fundamental theorem fits into the context of calculus because it applies derivatives and antiderivatives as well as integrals together. It will also help me with the applications of derivatives because know we can find not only the maximums and minimums but we can find the inbetween. The notation connects to what we have already learned because it applies Dy/Dx and Dx. Overall the fundamental theorem of calculus brings together the chapter four and chapter five stuff.
This week we learned chapter 5 section three which is about definite integrals using antiderivatives. The first thing we learned in section 5.3 was the rules for definite integrals. I found that I understand the rules of integrals pretty well. In an integral at the bottom of the notation is the smaller number also known as A and on top is bigger number know as B. The goal of an integral is to find the area of a section of a graph. To find an integral you can either use Nint on the calculator or do it by hand. We learned how to do the integral by hand by antideriving the function and then subtracting F(B)-F(A). We Also learned how to find the average value. To find the average value you have to do 1/(B-A) multiplied by the integregal. I have found that chapter 5 is way easier than chapter 4. I did not really understand chapter 4 very well so I wasn't very motivated to do the homework because everytime I did it I got really frustrated because I didn’t know how to do it . However with chapter 5 I have been more motivated to do my homework because I actually know how to do it.