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 F(x) = SRe)dt symbolizes a...

Extracted text: 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 F(x) = SRe)dt symbolizes a signed area function. This function evaluates the signed area under the curve between o and x. Note that on the left-hand side of the =, the variable is x. The i on the right-hand side is a "dummy variable" that represents all the values that x may take. You can call this dummy variable anything you like without changing fx), AS LONG AS you don't call the dummy variable x again! For example, F(x) = SAdt = SEAu)du = fõN)ds. You should NOT write F(x) = SZlidx. 1. Let y = Ax) = x2. Then consider the signed area function F(x) = S%,K)dt, which you know %3D represents the signed area below the curve from o to x. For example, F(2) represents the area below the curve y = f from 0 to 2, as show below: A. Using your graphing calculator to numerically approximate the definite integrals, complete the data chart below: x F(x) = fZROdt 1 2 3