Solve with integrating an implicit function

06202014, 02:40 PM
Post: #1




Solve with integrating an implicit function
I recently came, by chance, across this interesting post from one of the hpmuseum archives, originally posted by Valentin Albillo
********************************************** Test 7  Solving a definite integral of an implicit function: Find X in [0,1] such that /X   y(x).dx = 1/3  /0 where y(x) is an ultraradical function (a member of the family of elliptic functions) implicitly defined by: 5 y + y = x using precisions of 1E3 and 1E6 for the integral. HP71B code: X=FNROOT(0,1,INTEGRAL(O,FVAR,1E3,FNROOT(0,1,FVAR^5+FVARIVAR))1/3) this gives: X = 0.854136725005 in 433 seconds (precision = 1E3) = 0.854138746461 in 771 seconds (precision = 1E6) ************************************************ Obviously, this is very easy on the HP 71B, but it is also no problem for my HP 50G, with the following code << > x << 'Y^5+Y=x' 'Y' {0 1} ROOT >> >> 'FY' STO << << 0 X 'FY(Z)' 'Z' \int 1 3 /  >> 'X' {0 1} ROOT >> EVAL (and setting Number Format to Fix 3 or Fix 6 in the Mode Menu). However, I run into problems with the HP Prime Choosing 'FY' as a CAS program (y) > BEGIN RETURN(nSolve((t^5+t)=y , t)); END; So far, so good: FY(x), x real, with nSolve gives me the one real solution, as I'm not interested in the four complex ones (which would pop up with, say, fsolve). But now nSolve(int(FY(z),z,0,x)1/3=0,x) doesn't work, because FY can't take a symbolic argument (i.e., z). Or can it? Any suggestions? There must be a simple way of doing this on the Prime, but my brain is stuck trying to translate this from HP50G syntax. 

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