## Computer programming using Matlab or Freemat MTH 174 – Computer Project 2

Computer programming using Matlab or Freemat

MTH 174 – Computer Project 2

Use numerical integration to approximation of the definite integral using the listed below:

1. Methods:

(a) Simpson’s Rule (computer project 1)

(b) Composite Midpoint Rule

Z b

a

f(x)dx = (b

a)h2

24 f00(

a + b

2 ) + h

X

N

i=1

f(

xi+1 + xi

2 )

where h = (b

a)/N.

2. Alternative Extended Simpson’s Rule

Z b

a

f(x)dx = h

48 {17f(x1) + 59f(x2) + 43f(x3) + 49f(x4)

+48 “N

X3

i=5

f(xi)

#

+ 49f(xN2)

+ 43f(xN1)

+ 59f(xN ) + 17f(xN+1)

where h = (b

a)/N.

3. Use Simpson’s Rule, Composite Midpoint Method and Alternative Extended Simpson’s

Rule to approximate the following integral. Find the minimum N to yield a correct 4

decimal places correctly? Note only use N as an even counting number and START with

N = 8 and a = 0.0000000001

(a) Z ?/2

a

x

sin(x)

dx

(b) Z ?/2

a

ex

1

sin(x)

dx

(c) Z 1

a

arcsin(x)

x

dx

4. Use the three-methods above, write codes to compute the arc length of f(x) on [a, b] and

volume of f(x) on interval [a, b] revolve along x-axis. What is the minimum N to yield a

correct 4 decimal places correctly?

(a) f(x) = x

sin(x) from [a, ?/2]

(b) f(x) = ex

1

sin(x) from [a, ?/2]

(c) f(x) = arcsin(x)

x from [a, 1]

RUBRIC:

+ Hard copy of the report is due on March 30, 2017 by 7:45pm NO LATE WORK ACCEPTED.

+ Answers all questions and label it.

+ Must type and print all work follow by all code attached at the back of the report.

+ You may work with one partner

+ You turn in as many draft as possible to receive 100% no later than March 23, 2017