AP Calc: Week 20 - Integrals and Stuff

This week we learned about the fundamental theorem of calculus, and other things relating to integrals. We learned how to solve them by hand, and we learned that the integral of a function on an interval is the same as the area under the curve of that function on that interval. This was all very confusing at first, but it began to make sense after a while. The part that makes it difficult is many times, the questions look identical but are asking two different things. Even when we did the review assignment, all of the problems in each section looked similar, but were totally different. The math itself isn’t hard at all, it’s just hard to remember what formula to use for which question.

This chapter has really helped me with a concept I have really struggled with: finding the antiderivative of a function. Up until recently, I still had no idea at all how to find an antiderivative. Thankfully, since we have to do it for most of these problems, I have found that I am having a much better time understanding how to solve them. It really helps to know the rule where you add one to the power, and divide the new power by the number before x. This helps a TON. Also, I’m starting to see how negative exponents create a fraction, and how to use them to make it easier to find the derivative. One of the big things I still struggle with is the antiderivative of 1/x. If you use the rule I talked about earlier, it would be x^-1. Then add one to the power, so it’s x^0, then you’d have to divide 1/0, which is undefined. Fortunately, Mr. Cresswell explained that there is a rule for 1/x, and that is lnx. Why? I’m not really sure, I just know it works, and I’ll just have to live with that for now.