Question

and the r-axis. 5. Consider the region S bounded by r 1, r = 5, y (a) Use four rectangles and a Riemann sum to approximate the area of the region S. Sketch the region S and the rectangles and indicate your rectangles overestimate or underestimate the area of S. (b) Find an expression for the area of the region S as a limit. Do not evaluate the limit.

Answer 1

Answer:

What is Reimann Sum:

A Riemann Sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral. It may also be used to define the integration operation. ... Note that in the limit as n approaches infinity, the left-hand and right-hand Riemann sums become equal.

Types of reimann sum-

there are two types of reimann sum

1.Left Reimann sum

2.Right Reimann sum

Left Reimann Sum:

To make a Riemann sum, we must choose how we're going to make our rectangles. One possible choice is to make our rectangles touch the curve with their top-left corners. This is called a left Riemann sum.

Right Reimann Sum:

Another choice is to make our rectangles touch the curve with their top-right corners. This is the right Riemann sum.

Area and limit function of the graph is given below in solution...

Regions 2 2 3 4 using alet sum. becouuse the Left ciele top coY ner Yeimann gn this vion we cme given graph rectengles touehing And these 4 tne ore exkimathug aing CYe cver outside fue grafph. because Che tue megio Area of tne 5 SET -24 chi -Z+1 -1 A region tuis limit C lim che Aue 24