Chapter B, Problem 9E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

**Comparing Riemann Sums** Consider a triangle of area 2 square units bounded by the graphs of *y* = *x*, *y* = 0, and *x* = 2.

(a) Sketch the graph of the region.

(b) Divide the interval [0, 2] into *n* equal subintervals and show that the endpoints of the subintervals are

(c) Show that the left Riemann sum is

(d) Show that the right Riemann sum is

(e) Use a graphing utility and the program in Example 4 to complete the table.

n |
5 | 10 | 50 | 100 |

Left sum, S_{L} |
||||

Left sum, S_{R} |

(f) Show that

**(a)**

To determine

**To graph:** The region bounded by the graphs of

Explanation

**Given information:**

The area of the triangle is 2 square units and the equations are

**Graph:**

For equation

Put

Put

The table show the plotted points of line

**(b)**

To determine

The interval *n* equal subintervals and show that the endpoints of the subintervals are

**(c)**

To determine

**To prove:** The left Riemann sum is

**(d)**

To determine

**To prove:** The right Riemann sum is

**(e)**

To determine

**To fill:** The table shown below by a graphing utility.

**(f)**

To determine

**To prove:** The

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