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+--- Thread: Calculating area graphically on the HP50g appears inaccurate (/thread-1204.html)
Calculating area graphically on the HP50g appears inaccurate - cdecastro - 04-30-2014 09:24 AM
If I graph the function y=sin(x), find the root at x=0 using FCN->ROOT, set the mark (via "X"), find the zero at Pi again using the root function, then request the AREA, I get the answer 1.99913515027 rather than 2. I am assuming the calculator is not really moving the end mark to Pi but rather to the x value of the nearest approximating pixel (with respect to the scaling in the current plot window). Is this correct? If so, graphically computing areas should not to be considered as accurate as the evaluation of the corresponding definite integral. Thanks in advance for your assistance.
Appreciatively,
Chris
RE: Calculating area graphically on the HP50g appears inaccurate - Han - 04-30-2014 03:47 PM
(04-30-2014 09:24 AM)cdecastro Wrote: If I graph the function y=sin(x), find the root at x=0 using FCN->ROOT, set the mark (via "X"), find the zero at Pi again using the root function, then request the AREA, I get the answer 1.99913515027 rather than 2. I am assuming the calculator is not really moving the end mark to Pi but rather to the x value of the nearest approximating pixel (with respect to the scaling in the current plot window). Is this correct? If so, graphically computing areas should not to be considered as accurate as the evaluation of the corresponding definite integral. Thanks in advance for your assistance.
Appreciatively,
Chris
I thought this (the bold statement) was always true even without the use of calculators (e.g. draw a graph, cut the area out on paper, and weigh vs. area of a unit square). Most numerical algorithms are only approximations. If you want the exact area, use the built-in CAS.
RE: Calculating area graphically on the HP50g appears inaccurate - cdecastro - 04-30-2014 04:00 PM
Thanks for the reply Han. Of course, I understand your point. My issue is that if I perform the integration (numerical or otherwise) using the limits found by ROOT I would expect the value to agree (to the limits of accuracy of the device) in both contexts. I.E. I would have gotten the same numerical value using the AREA function as I would using the calculators numerical integration procedure.
Thanks,
Chris
RE: Calculating area graphically on the HP50g appears inaccurate - Han - 04-30-2014 04:28 PM
I see what you mean now. Yes, your original suspicion is correct. The AREA function in the graph view uses the actual x-values where the cursor is located. Thus, when you find the root, the cursor is moved to the pixel closest to the actual root. In this case, using the default settings, the cursor is placed at x=3.1 while the ROOT function returns a more precise result. The AREA function is simply giving the area between x=0 and x=3.1.
RE: Calculating area graphically on the HP50g appears inaccurate - Wes Loewer - 05-01-2014 07:52 PM
(04-30-2014 04:28 PM)Han Wrote: The AREA function in the graph view uses the actual x-values where the cursor is located.
I always thought this behavior made that feature on the 50g rather useless. If you can't specify the limits precisely, what's the point?
RE: Calculating area graphically on the HP50g appears inaccurate - Alvaro - 05-01-2014 08:31 PM
(05-01-2014 07:52 PM)Wes Loewer Wrote:(04-30-2014 04:28 PM)Han Wrote: The AREA function in the graph view uses the actual x-values where the cursor is located.
I always thought this behavior made that feature on the 50g rather useless. If you can't specify the limits precisely, what's the point?
it means that is not possible to calculate a AREA between any given x1 and x2?
At least is there the possibility that the actual cursor position is beeing displayed?