Accumulated Change vs. Definite Integral

Martyna Wiacek MTH 116 C- Applied Calculus 11/6/2012 Chapter 5 Writing Assignment There is a correlation amidst sphere, stash away metamorphose, and the definite integral that we have focused on throughout Chapter 5 in Applied Calculus. When looking at one rate-of- deviate accountability, the collect change over an interval and the definite integral are equivalent, their values could be positive, negative or zero. However, the area could never be negative because area is always positive by definition. The collect change looks at the all area of the pass away that is between the graph 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 specific 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 accretion of change in a certain function can be evaluated by using the area of the region between the rate-of-change curve and the horizontal axis.We likewise see a similar relationship between the rate-of-change graph and the accumulated graph that we saw in derivatives. A stripped-down in the accumulated graph is caused by the rate-of-change function crossing over from positive to negative. A maximum in the accumulated graph is a result of the rate-of-change function moving from negative to positive. When there is a maximum or minimum in the rate-of-change graph you get an inflection point in the aggregation graph as well. Also, we see that if the rate-of-change function is negative then the accumulated graph is negative and so the assembly graph is decreasing.However, when the rate-of-change graph is increasing, it does not affect 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 transmission line 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 go Part A Use a grid to count boxes and foretell the accumulated area from 1 to x for values of x space 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 Part B Sketch the graph of the accumulation function based on the table values Part C Write the mathematical notation for the function sketched in part b Part D Write a sentence of interpretation for the accumulation form 0 to 6 hours After 6 hours of rainfall in Florida, the amount of rain should accumulate to an estimate of 2. 4 inches.