### Home > CALC > Chapter 1 > Lesson 1.2.3 > Problem 1-58

Using left endpoint rectangles. The first two rectangles are shown.

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

.Sketch the remaining rectangle. Notice: The height of the LAST rectangle is evaluated at

(not).Each rectangle has a base of

and a height of . Area_____________ Using right endpoint rectangles.

Notice: The height of the FIRST rectangle is evaluated at

. The height of the LAST rectangle is evaluated at.Each rectangle has a base of

and a height of . Area_____________ Using trapezoids. What do you notice? Does this always happen?

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*