Timeline for Help on script for parametric surface integral
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2020 at 6:03 | comment | added | JDVC | Many thanks. I'm sincerely grateful. | |
| Dec 28, 2020 at 5:47 | comment | added | cvgmt |
@BRC We can use NIntegrate instead of Integrate to calculate the numeric value. x[u_, v_] := u Cos[v]; y[u_, v_] := u Sin[v]; z[u_, v_] := v; r[u_, v_] := {x[u, v], y[u, v], z[u, v]}; reg = ParametricRegion[r[u, v], {{u, 0, 1}, {v, 0, Pi/2}}]; NIntegrate[y, Element[{x, y, z}, reg]]
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| Dec 28, 2020 at 5:11 | comment | added | JDVC | Thanks so much for your generous time and effort. But the integrand in your problem is x + y. What if it is just "y"? As in the following, which doesn't compute: x[u_, v_] := u Cos[v]; y[u_, v_] := u Sin[v]; z[u_, v_] := v; r[u_, v_] := {x[u, v], y[u, v], z[u, v]}; reg = ParametricRegion[r[u, v], {{u, 0, 1}, {v, 0, Pi/2}}]; Integrate[y, {x, y, z} [Element] reg] | |
| Dec 28, 2020 at 5:07 | comment | added | cvgmt |
@BRC x[u_, v_] := u + v; y[u_, v_] := u - v; r[u_, v_] := {x[u, v], y[u, v]}; reg = ParametricRegion[r[u, v], {{u, 0, 2}, {v, 0, 1}}]; Integrate[x + y, {x, y} \[Element] reg]
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| Dec 28, 2020 at 4:55 | comment | added | JDVC | Perhaps if I just have a single (or even two )variable in the integrand (all of the other problems had x, y, and z), I need some kind of placeholder for the missing variable? | |
| Dec 28, 2020 at 4:51 | comment | added | JDVC | I tried that, alas. If you make the integrand something with just one variable, would that make the code unworkable? For example, in a similar problem to "Update' above, I changed the integrand to just "y" and it gave me gobbledygook: \!(*UnderscriptBox[([Integral]), ({x, y, z} [Element] ParametricRegion[{{Cos[v]\ u, u\ Sin[v], v}, 0 [LessEqual] u [LessEqual] 1 && 0 [LessEqual] v [LessEqual] *FractionBox[([Pi]), (2)]}, {u, v}])])y | |
| Dec 28, 2020 at 4:39 | comment | added | cvgmt | @BRC You can use Clear["`*"]; to clear the variable before the new evaluation. | |
| Dec 28, 2020 at 4:34 | comment | added | JDVC | And this code doesn't seem (?) to work if the parameters are trig functions. I get strange message when I use trig functions in the parameters. Is that right? | |
| Dec 28, 2020 at 4:21 | comment | added | JDVC | Thanks so much for the code. It is very helpful. See my update above, if you can, and perhaps you can clarify? | |
| Dec 28, 2020 at 2:35 | vote | accept | JDVC | ||
| Dec 28, 2020 at 2:16 | history | answered | cvgmt | CC BY-SA 4.0 |