
Home > CALC > Chapter 1 > Lesson 1.2.3 > Problem 1-58
Regarding the word ESTIMATE: You are not being asked to make a guess. You still need to compute. Of course, the area using rectangles is an approximation of the actual area under f(x).
Sketch the remaining rectangle. Notice: The height of the LAST rectangle is evaluated at x = 2 (not x = 3).
Each rectangle has a base of 1 and a height of f(x). Area = 1(f(−3) + f(−2) + f(−1) + f(0) + f(1) + f(2)) =_____________
Notice: The height of the FIRST rectangle is evaluated at x = −2. The height of the LAST rectangle is evaluated at x = 3.
Each rectangle has a base of 1 and a height of f(x). Area = 1( f(-2) + f(-1) + f(0) + f(1) + f(2) + f(3)) =_____________
The trapezoidal sum is the AVERAGE of the left- and right-endpoint sums! Expain why this happens (algebraically and geometrically).
Use the eTool below to view the graphs.
Click the link at right for the full version of the eTool: Calc 1-58 HW eTool