t f(t) Num. Integration 1 Error

0 00.052 0.103813 0.0026991282247 0.002702 0.0009023093 0.9924360.12 0.237703 0.0143106467402 0.014331 0.00142312460.27 0.514136 0.0706985430962 0.071146 0.00632426360.33 0.613117 0.104516128405 0.105004 0.00466679980.47 0.807558 0.2039633750715 0.205106 0.0056020470.521 0.863415 0.2465731876599 0.247753 0.00478394920.598 0.930582 0.3156420777342 0.316958 0.0041706140.71 0.988652 0.4231191797945 0.424887 0.00417869320.8 0.999574 0.5125893212597 0.5146 0.0039221260.95 0.9463 0.6585298480644 0.661645 0.00473013540.99 0.917438 0.6958046089238 0.698939 0.0045053281.15 0.745705 0.8288560623204 0.833138 0.0051660941.3 0.515501 0.9234465561203 0.928444 0.00541213841.33 0.463191 0.9381269456716 0.943129 0.00533214221.42 0.297041 0.9723374134023 0.977432 0.00523984241.5 0.14112 0.9898638677769 0.994996 0.00518493571.62 -0.098249 0.9924361526358 0.997581 0.0051840101

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8-0.2

0

0.2

0.4

0.6

0.8

1

1.2

f(t) vs. t

t

f(t)

Roy Haggerty:Numerical integration from A3B3 to A21B21using trapezoidal rule. This is a more sophisticated way to implement the same numerical integration as given along column C, but it saves space and work. Note the answer is the same as given in cell C21, however.

You may copy the equation from this cell and implement it in your spreadsheet. Be careful, however, to modify the first and last cell locations properly.

Roy Haggerty:Function of time: use sine function as example: f(t) = v0 sin(w t)

Roy Haggerty:This is the numerical integration along the function using the "trapezoidal rule".The value shown is the integral from the origin to the time given in that row.

For your numerical integration, you will want to copy the equation from C5 to your excel spreadsheet. Be careful that references in equation are correct - i.e., you may need to modify references to rows or columns to match your data.

Roy Haggerty:This is the integral of the function from 0 to 1.62.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8-0.2

0

0.2

0.4

0.6

0.8

1

1.2

f(t) vs. t

t

f(t)

0 0 0 0 #DIV/0!

v0= 1w= 2

Roy Haggerty:Numerical integration from A3B3 to A21B21using trapezoidal rule. This is a more sophisticated way to implement the same numerical integration as given along column C, but it saves space and work. Note the answer is the same as given in cell C21, however.

You may copy the equation from this cell and implement it in your spreadsheet. Be careful, however, to modify the first and last cell locations properly.

Roy Haggerty:This is the numerical integration along the function using the "trapezoidal rule".The value shown is the integral from the origin to the time given in that row.

For your numerical integration, you will want to copy the equation from C5 to your excel spreadsheet. Be careful that references in equation are correct - i.e., you may need to modify references to rows or columns to match your data.

Roy Haggerty:This is the second parameter used in the trigonometric equation in Column B.

Changing this value is equivalent to changing the spacing between the time data points. You may modify this and see how the integration's accuracy changes (as well as the function).