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Category: EECS 2510

Description

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In your first project you will use Simpson’s rule to determine the integral of a function over an interval.

The user will input a lower value for x (a), an upper value for x (b), and a number of steps that should

be used to compute the step size, h. Your program will compute the integral over the range using the

given step size and report the value. Your intermediate data will be output in a table.

Details:

Simpson’s ⅜ rule allows us to approximate a value for a function. If the function were sin(x) where x is

in radians and our lower value was 0.0, our upper value is 3.14159, and a step size of h of 0.1570795.

Simpson’s rule finds the integral over this interval as:

Simpson’s 3/8 Rule — Sample Calculation for f(x) = sin(x)

h 0.1570795

a b = a + h f(a)

f((2a +

b)/3)

f((a+2*b)/

3) f(b)

value = (b-a)/8 * (f(a) + 3 * f((2a+b)/3) + 3 * f((a + 2 *

b)/3) + f(b))

0.00000 0.15708 0.00000 0.05234 0.10453 0.15643 0.01231

0.15708 0.31416 0.15643 0.20791 0.25882 0.30902 0.03663

0.31416 0.47124 0.30902 0.35837 0.40674 0.45399 0.06005

0.47124 0.62832 0.45399 0.50000 0.54464 0.58778 0.08199

0.62832 0.78540 0.58778 0.62932 0.66913 0.70711 0.10191

0.78540 0.94248 0.70711 0.74314 0.77715 0.80902 0.11932

0.94248 1.09956 0.80902 0.83867 0.86602 0.89101 0.13379

1.09956 1.25664 0.89101 0.91355 0.93358 0.95106 0.14497

1.25664 1.41372 0.95106 0.96593 0.97815 0.98769 0.15258

1.41372 1.57080 0.98769 0.99452 0.99863 1.00000 0.15643

1.57080 1.72787 1.00000 0.99863 0.99452 0.98769 0.15643

1.72787 1.88495 0.98769 0.97815 0.96593 0.95106 0.15258

1.88495 2.04203 0.95106 0.93358 0.91355 0.89101 0.14497

2.04203 2.19911 0.89101 0.86603 0.83867 0.80902 0.13379

2.19911 2.35619 0.80902 0.77715 0.74315 0.70711 0.11932

2.35619 2.51327 0.70711 0.66913 0.62932 0.58779 0.10191

2.51327 2.67035 0.58779 0.54464 0.50000 0.45399 0.08199

2.67035 2.82743 0.45399 0.40674 0.35837 0.30902 0.06005

2.82743 2.98451 0.30902 0.25882 0.20791 0.15644 0.03663

2.98451 3.14159 0.15644 0.10453 0.05234 0.00000 0.01231

2.00000

Your program should allow the user to put in the starting value (a), the ending value (b), and the

number of steps to do (in this case we have 20 steps). The step size above is (b-a)/20. It should then

calculate the values and for each interval it should output the values of a, b, and Simpson’s ⅜ rule for

each interval. At the end, the total of the values should be reported and your program should exit.

EECS 2510: Project 1 1 Spring 2018

Hints and Advice:

Do it in little pieces. Do the input of the values and make sure they are coming in the way you expect

first. Compute the value for one small interval and test it. You can use the data in the table above to

help you test it. Finally, start doing all the intervals and compute the sum.

Submission:

Your source files (.cpp, .h, .hpp) should be submitted online in BlackBoard. I need only your source

files. You do not need to zip them together to submit them.

EECS 2510: Project 1 2 Spring 2018

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