This week we began learning about and working with different methods of estimating the total area under a curve. The activity that we worked on in class when we began learning about this concept was really enjoyable for me and I think that it helped me to gain a better understanding of the concept. It showed that we can use small shapes that we can easily find the area of to estimate the area of a strange, abstract shape, and that the smaller we make the shapes, the more accurate our estimation is to the actual area. From another activity we were able to discover that the area under a velocity curve represents the distance traveled.
We have been focusing on RAM (Rectangular Approximation Method), where rectangles are used to help approximate the area under a curve. We can use this method by placing the right corner, midpoint, or left corner of the the rectangles on the curve. When the curve is increasing, RRAM will be an overestimation of the area because the rectangles will extend above the curve, but the opposite will be true when the curve is decreasing. On the other hand, when the curve is increasing, LRAM will be an underestimation of the area because the rectangles are completely under the curve and some space is not accounted for, but the opposite is true when the curve is decreasing. MRAM may be the most accurate method of estimating the area because part of the rectangles extend above the curve, yet some space under the curve remains unaccounted for.
We have been focusing on RAM (Rectangular Approximation Method), where rectangles are used to help approximate the area under a curve. We can use this method by placing the right corner, midpoint, or left corner of the the rectangles on the curve. When the curve is increasing, RRAM will be an overestimation of the area because the rectangles will extend above the curve, but the opposite will be true when the curve is decreasing. On the other hand, when the curve is increasing, LRAM will be an underestimation of the area because the rectangles are completely under the curve and some space is not accounted for, but the opposite is true when the curve is decreasing. MRAM may be the most accurate method of estimating the area because part of the rectangles extend above the curve, yet some space under the curve remains unaccounted for.
After completing the activities and assignment for estimating finite sums, I feel pretty good about this concept, but I am curious as to what method we will learn when we get back from break. I think there must be an easier way or a trick to finding the area rather than manually adding up the area of rectangles under the curve. I am looking forward to learning more about this when we get back and how we can find even more accurate estimations of the area under curves.