Home |
Search |
Today's Posts |
#1
Posted to microsoft.public.excel.misc
|
|||
|
|||
How to use an integral for cell output value.
Suppose in the A column, I have a column of data in cells A(1) to A(10).
I would like the output data in cells B(1) to B(10) to be given by the formula: B(N) = Integral of f(x)dx, evaluated from 0 to 10. Where f(x) = sin[A(N) * pi * x / 10] This integral gives a real # in all cases; my hand-held calculator can solve them, but it's tedious to do each calculation individually (because in reality I have way more than 10 values I need to solve). Iit would be handy if I could have excel do this calculation for me, but I can't figure out how to make excel use an integral for the output of column (B). Can I do this easily? |
#2
Posted to microsoft.public.excel.misc
|
|||
|
|||
How to use an integral for cell output value.
Not sure if this is right, but by using the equations below the following
results are obtained ROW: COL A COL B Fomula in column B 1 0 0 2 1 0.28173 =SIN(A2*PI()*((A2-A1)/COUNT(A:A))) 3 2 0.54064 =SIN(A3*PI()*((A3-A2)/COUNT(A:A))) 4 3 0.75575 =SIN(A4*PI()*((A4-A3)/COUNT(A:A))) 5 4 0.90963 =SIN(A5*PI()*((A5-A4)/COUNT(A:A))) 6 5 0.98982 =SIN(A6*PI()*((A6-A5)/COUNT(A:A))) 7 6 0.98982 =SIN(A7*PI()*((A7-A6)/COUNT(A:A))) 8 7 0.90963 =SIN(A8*PI()*((A8-A7)/COUNT(A:A))) 9 8 0.75575 =SIN(A9*PI()*((A9-A8)/COUNT(A:A))) 10 9 0.54064 =SIN(A10*PI()*((A10-A9)/COUNT(A:A))) 11 10 0.28173 =SIN(A11*PI()*((A11-A10)/COUNT(A:A))) The formula can be dragged down as many cells is as there is data in column A... Is this what you expected? -- Kind regards Rik "Corribus" wrote: Suppose in the A column, I have a column of data in cells A(1) to A(10). I would like the output data in cells B(1) to B(10) to be given by the formula: B(N) = Integral of f(x)dx, evaluated from 0 to 10. Where f(x) = sin[A(N) * pi * x / 10] This integral gives a real # in all cases; my hand-held calculator can solve them, but it's tedious to do each calculation individually (because in reality I have way more than 10 values I need to solve). Iit would be handy if I could have excel do this calculation for me, but I can't figure out how to make excel use an integral for the output of column (B). Can I do this easily? |
#3
Posted to microsoft.public.excel.misc
|
|||
|
|||
How to use an integral for cell output value.
Hi Rik -
Thanks for the reply. Unfortunately, the output values are not correct. For example, if the input in column A is 1 (as it is in row, 2), the output value in the associated B column should be Integral of: sin(pi * x / 10), evaluated from 0 to 10 Which, according to my calculation, should be 6.36619 Likewise, for A = 2, B = 0; A = 3, B = 2.12206; etc. Obviously, in the case of the present formula, it's pretty simple for me to evaluate these by hand. The formula I really need to use is a bit more tedious to integrate by hand, however. The current (simplified) example is just for me to learn how to use an integration as an output - if such a thing is even possible. "Rik_UK" wrote: Not sure if this is right, but by using the equations below the following results are obtained ROW: COL A COL B Fomula in column B 1 0 0 2 1 0.28173 =SIN(A2*PI()*((A2-A1)/COUNT(A:A))) 3 2 0.54064 =SIN(A3*PI()*((A3-A2)/COUNT(A:A))) 4 3 0.75575 =SIN(A4*PI()*((A4-A3)/COUNT(A:A))) 5 4 0.90963 =SIN(A5*PI()*((A5-A4)/COUNT(A:A))) 6 5 0.98982 =SIN(A6*PI()*((A6-A5)/COUNT(A:A))) 7 6 0.98982 =SIN(A7*PI()*((A7-A6)/COUNT(A:A))) 8 7 0.90963 =SIN(A8*PI()*((A8-A7)/COUNT(A:A))) 9 8 0.75575 =SIN(A9*PI()*((A9-A8)/COUNT(A:A))) 10 9 0.54064 =SIN(A10*PI()*((A10-A9)/COUNT(A:A))) 11 10 0.28173 =SIN(A11*PI()*((A11-A10)/COUNT(A:A))) The formula can be dragged down as many cells is as there is data in column A... Is this what you expected? -- Kind regards Rik "Corribus" wrote: Suppose in the A column, I have a column of data in cells A(1) to A(10). I would like the output data in cells B(1) to B(10) to be given by the formula: B(N) = Integral of f(x)dx, evaluated from 0 to 10. Where f(x) = sin[A(N) * pi * x / 10] This integral gives a real # in all cases; my hand-held calculator can solve them, but it's tedious to do each calculation individually (because in reality I have way more than 10 values I need to solve). Iit would be handy if I could have excel do this calculation for me, but I can't figure out how to make excel use an integral for the output of column (B). Can I do this easily? |
#4
Posted to microsoft.public.excel.misc
|
|||
|
|||
How to use an integral for cell output value.
I think that Rik may have intended his formula to be
=SIN(A2*PI()/10)*(A2-A1) If you use an interval of 1, as Rik did, the terms of the above formula sum to 6.313752 If you change the interval to 0.1, the sum becomes 6.365754 As you are no doubt aware, the integral of x is the limit of the sum of (x * dx) as dx tends to zero, so you can make the interval progressively smaller. With an interval of 0.01, the sum is 6.366192. You are better, of course, to say that the result of the integral is 20/PI() [and thus get 6.366198], rather than doing the numerical integration. -- David Biddulph "Corribus" wrote in message ... Hi Rik - Thanks for the reply. Unfortunately, the output values are not correct. For example, if the input in column A is 1 (as it is in row, 2), the output value in the associated B column should be Integral of: sin(pi * x / 10), evaluated from 0 to 10 Which, according to my calculation, should be 6.36619 Likewise, for A = 2, B = 0; A = 3, B = 2.12206; etc. Obviously, in the case of the present formula, it's pretty simple for me to evaluate these by hand. The formula I really need to use is a bit more tedious to integrate by hand, however. The current (simplified) example is just for me to learn how to use an integration as an output - if such a thing is even possible. "Rik_UK" wrote: Not sure if this is right, but by using the equations below the following results are obtained ROW: COL A COL B Fomula in column B 1 0 0 2 1 0.28173 =SIN(A2*PI()*((A2-A1)/COUNT(A:A))) 3 2 0.54064 =SIN(A3*PI()*((A3-A2)/COUNT(A:A))) 4 3 0.75575 =SIN(A4*PI()*((A4-A3)/COUNT(A:A))) 5 4 0.90963 =SIN(A5*PI()*((A5-A4)/COUNT(A:A))) 6 5 0.98982 =SIN(A6*PI()*((A6-A5)/COUNT(A:A))) 7 6 0.98982 =SIN(A7*PI()*((A7-A6)/COUNT(A:A))) 8 7 0.90963 =SIN(A8*PI()*((A8-A7)/COUNT(A:A))) 9 8 0.75575 =SIN(A9*PI()*((A9-A8)/COUNT(A:A))) 10 9 0.54064 =SIN(A10*PI()*((A10-A9)/COUNT(A:A))) 11 10 0.28173 =SIN(A11*PI()*((A11-A10)/COUNT(A:A))) The formula can be dragged down as many cells is as there is data in column A... Is this what you expected? -- Kind regards Rik "Corribus" wrote: Suppose in the A column, I have a column of data in cells A(1) to A(10). I would like the output data in cells B(1) to B(10) to be given by the formula: B(N) = Integral of f(x)dx, evaluated from 0 to 10. Where f(x) = sin[A(N) * pi * x / 10] This integral gives a real # in all cases; my hand-held calculator can solve them, but it's tedious to do each calculation individually (because in reality I have way more than 10 values I need to solve). Iit would be handy if I could have excel do this calculation for me, but I can't figure out how to make excel use an integral for the output of column (B). Can I do this easily? |
#5
Posted to microsoft.public.excel.misc
|
|||
|
|||
How to use an integral for cell output value.
Ah, I see - I didn't check his formula, just noticed the answers didn't look
right. Thank you for the help, that makes sense. "David Biddulph" wrote: I think that Rik may have intended his formula to be =SIN(A2*PI()/10)*(A2-A1) If you use an interval of 1, as Rik did, the terms of the above formula sum to 6.313752 If you change the interval to 0.1, the sum becomes 6.365754 As you are no doubt aware, the integral of x is the limit of the sum of (x * dx) as dx tends to zero, so you can make the interval progressively smaller. With an interval of 0.01, the sum is 6.366192. You are better, of course, to say that the result of the integral is 20/PI() [and thus get 6.366198], rather than doing the numerical integration. -- David Biddulph "Corribus" wrote in message ... Hi Rik - Thanks for the reply. Unfortunately, the output values are not correct. For example, if the input in column A is 1 (as it is in row, 2), the output value in the associated B column should be Integral of: sin(pi * x / 10), evaluated from 0 to 10 Which, according to my calculation, should be 6.36619 Likewise, for A = 2, B = 0; A = 3, B = 2.12206; etc. Obviously, in the case of the present formula, it's pretty simple for me to evaluate these by hand. The formula I really need to use is a bit more tedious to integrate by hand, however. The current (simplified) example is just for me to learn how to use an integration as an output - if such a thing is even possible. "Rik_UK" wrote: Not sure if this is right, but by using the equations below the following results are obtained ROW: COL A COL B Fomula in column B 1 0 0 2 1 0.28173 =SIN(A2*PI()*((A2-A1)/COUNT(A:A))) 3 2 0.54064 =SIN(A3*PI()*((A3-A2)/COUNT(A:A))) 4 3 0.75575 =SIN(A4*PI()*((A4-A3)/COUNT(A:A))) 5 4 0.90963 =SIN(A5*PI()*((A5-A4)/COUNT(A:A))) 6 5 0.98982 =SIN(A6*PI()*((A6-A5)/COUNT(A:A))) 7 6 0.98982 =SIN(A7*PI()*((A7-A6)/COUNT(A:A))) 8 7 0.90963 =SIN(A8*PI()*((A8-A7)/COUNT(A:A))) 9 8 0.75575 =SIN(A9*PI()*((A9-A8)/COUNT(A:A))) 10 9 0.54064 =SIN(A10*PI()*((A10-A9)/COUNT(A:A))) 11 10 0.28173 =SIN(A11*PI()*((A11-A10)/COUNT(A:A))) The formula can be dragged down as many cells is as there is data in column A... Is this what you expected? -- Kind regards Rik "Corribus" wrote: Suppose in the A column, I have a column of data in cells A(1) to A(10). I would like the output data in cells B(1) to B(10) to be given by the formula: B(N) = Integral of f(x)dx, evaluated from 0 to 10. Where f(x) = sin[A(N) * pi * x / 10] This integral gives a real # in all cases; my hand-held calculator can solve them, but it's tedious to do each calculation individually (because in reality I have way more than 10 values I need to solve). Iit would be handy if I could have excel do this calculation for me, but I can't figure out how to make excel use an integral for the output of column (B). Can I do this easily? . |
Reply |
Thread Tools | Search this Thread |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Forum | |||
definite integral | Excel Worksheet Functions | |||
How to do integral calculus in Excel spreadsheet? | Excel Worksheet Functions | |||
Include exponential (and exp-cosine-sine) integral maths functions | Excel Worksheet Functions | |||
How do I output the worksheet name in cell? | Excel Discussion (Misc queries) | |||
PDF output with Cell as filename | Excel Worksheet Functions |