M120 Project 3

Date due:                                                    25 points    [5 pt deduction for each class day late]

Objective:  Area as a Riemann Sum, Trapezoid and Simpson's Rule

1.  For the integral , use the 'rectangle rule' to find an approximation to the area

under the curve.

a)  Use  n = 6 and the 'sum of rectangles' method three different times, according to the  value of . Show your work. These should be done using no program other than EVALUATE or using the TABLE feature.

i)  Use   as the left endpoint and find the sum

ii)  Use   as the right endpoint and find the sum

iii)  Finally use  as the midpoint of each interval and find the sum.

b)  Use your program to find the approximation using Trapezoid and Simpson's with  n = 6.

2.  For each of the following intervals, use the 'rectangle rule', with   as the midpoint of the interval.  However, the value of n should vary.  You may use a program on your calculator to find the sum of the midpoint rectangles.

i)   Each integral should be evaluated for  n = 4, 10, 25, and 100.

ii)  Also each integral should be evaluated with Simpson's and Trapezoid for n  = 100.

iii)  If indicated, the integral should also be evaluated using techniques from chapters 6 & 7.

iv)  Use the built-in numeric-integral on your calculator also.

 a) b) c)     (Find exact value also) d)

You might make a table for parts a) through d) with column headings:

 n = 4 n = 10 n = 25 n = 100 Trapezoid Sum Simpson's Sum Using fnInt on Calculator