This week we began Chapter 5. Chapter 5 consists of definite integrals. This week we explored the first two sections of it that dealt with estimations of the area under a curved graph. The previous section that dealt with derivatives comes into play in this chapter. According to the book we have not learned the way to find anti dervatives, however because we skipped ahead and learned it before it helps understanding more clear on the purpose of integral area estimates. The purpose of this week was being able to find approximate areas for a "curvy thing."
I learned that there are three methods of finding the approximate areas to a curvy graph. The three ways are LRAM, MRAM, and RRAM. The differences between these three methods are where the points are placed on the graph while drawing in the intervals of rectangles. For example, LRAM values will have their points to the left of the interval rectangle, MRAM, will have their points in the middle between the two intervals, awhile RRAM, will have their's to the right. After figuring out the values and point placements you must find the areas of all the rectangles by using the width and height values for all intervals inside curve. Then you add all of the individual areas up to conclude to the estimated area of that curve. I thought MRAM was the easiest method to use, simply because it was easier to keep consistency. The other two methods, I struggled with because their approximations were not as accurate as MRAM and I found it harder to draw in the rectangles and not get it all jumbled up.
I believe my participation went well in class this week. I interacted with questions I had with you and the class. Next week, I plan to continue working on definite integrals and to go more in depth to really understand the concepts to help me prepare for the quiz/test.
Here are websites that helped me understand concepts better this week:
http://mathworld.wolfram.com/DefiniteIntegral.html
http://www.mathsisfun.com/calculus/integration-definite.html