Accumulated Change vs. Definite Integral

Martyna Wiacek MTH 116 C- Applied Calculus 11/6/2012 Chapter 5 piece Assignment in that location is a correlation between land, collect change, and the explicit integral that we have focused on throughout Chapter 5 in Applied Calculus. When looking at one rate-of-change character, the accumulated change everywhere an interval and the definite integral are equivalent, their values could be positive, damaging or zero. However, the eye socket could never be negative because area is ever so positive by definition. The accumulated change looks at the whole area of the share that is between the interpret and the horizontal axis.For instance, if f (x) is a rate-of-change function the area between f (x) and the x-axis represents the accumulated change between x = a and x = b. However, the definite integral puts particular proposition limits into the function and the area of a particular region can be determined. For example, if f (x) is a rate-of-change function it means that is what you can consider the area. The accumulation of change in a certain function can be evaluated by victimisation the area of the region between the rate-of-change curve and the horizontal axis.We also contain a similar relationship between the rate-of-change represent and the accumulated interpretical record that we saw in derivatives. A minimum in the accumulated represent is caused by the rate-of-change function crossing over from positive to negative. A utmost in the accumulated graph is a result of the rate-of-change function lamentable from negative to positive. When there is a maximum or minimum in the rate-of-change graph you get an inflection point in the accumulation graph as well. Also, we see that if the rate-of-change function is negative then the accumulated graph is negative and so the accumulation graph is decreasing.However, when the rate-of-change graph is increasing, it does not reach whether or not the accumulated graph is increasing or decreasing. There are several problems in our book that demonstrate this relationship. A specific example that I believe did a good job demonstrating it was The graph in the figure represents the rate of change of rainfall in Florida during a severe thunderstorm t hours after the rain began falling percentage A Use a grid to count boxes and estimate the accumulated area from 1 to x for values of x spaced 1 hour apart, starting at 0 and ending at 6.Record the estimates in a table. 0 0 1 . 4 2 . 65 3 1 4 1. 35 5 2 6 2. 4 partition B Sketch the graph of the accumulation function based on the table values Part C bring out the mathematical notation for the function sketched in part b Part D Write a sentence of interpretation for the accumulation score 0 to 6 hours After 6 hours of rainfall in Florida, the list of rain should accumulate to an estimate of 2. 4 inches.