AP Calculus Assignment: Exploring the Relationship Between the Derivative and the Antiderivative TI-83 and TI-84 Version NOTE: Area Functions and Area Function Notation The expression Fur) = Erja'r symbolizes a signed area function. This function evaluates the signed area under the curve between 0 and 3:. Note that on the left-hand side of the =, the variable is x. The r on the right-hand side is a \"dummy variable" that represents all the values that I may take. You can call this dummy variable anything you like without changing fix}, AS LONG AS you don't call the dummy variable 3: again! For exam Ier Fix) = [Jamar = Igum = [31min You should NOT write F(x) = gxm. 1. Let y = x) = x2. Then consider the signed area function F(x) 2 Igzyr, which you know represents the signed area below the curve from i] to 3:. For example, H2) represents the area below the curve 3; = ffrom 0 to 2, as show below: A. Using your graphing calculator to numerically approximate the denite integrals, complete the data chart below: AP Calculus Assignment: Exploring the Relationship Between the Derivative and the Antiderivative TI-BB and TI-B4 Version B. Now, you'll use your calculator to create an area function Rx). By \"area function," we mean a function where you enter an 35 value, and the output is the area under the curvex) = x2. "me function will be in the form '3be and will represent the area function Fibs). You can do this by doing a \"regression" on your calculator; enter your data points (from the table yOu lled in), and your calculator will try to find a function that matches those data points. On the 11-83, this is done by pressing STATIEDIT and then entering your data into the statistical register; x values go in L1' F[x) values go in L2. Then go STATICALCIA:P1.ereg, which will nd a function {in the form J: = axb] that ts your data points. (See pages 12-2? in the "IT-83 book if needed.) Remember that the calculator is approximating, so if it tells you that a = 12199999999 and b = 4100000001, it's legitimate to just take a = 123 and b = 12. 1I'our function approximating Fm is: Scoring (teacher will complete): Category Points Possible Points Earned Your equation for F{x} of the fonn axb 4 TOTAL 4 C. What is the relationship between y0ur function approximating HI) and the antiderivative of x) 2 x2; how are they similar and how are they different? Scoring (teacher will complete): Category Points Possible Points Earned Correct relationship between F(I) and the antiderivative afx) 3 TOTAL 3 D. Using the relationship you just described above and taking x) = 4x3 + 12;:2 +2x, take a guess at an equation for the function 10(fo = jxyr, the signed area function for f. In other words' take a guess at an area function that will give the area under the curve x) = 4x3 +12x2 +2x. Your guess. HI) = Irr =