Re: Sovling integrals: non-algebraic???

*To*: mathgroup at smc.vnet.net*Subject*: [mg35376] Re: [mg35369] Sovling integrals: non-algebraic???*From*: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>*Date*: Wed, 10 Jul 2002 02:19:42 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Your equation is: In[6]:= Integrate[(c x^d), {x, a, b}] ==y Out[6]= c*(-(a^(1 + d)/(1 + d)) + b^(1 + d)/(1 + d)) == y Solve cannot solve this because it is not meant to. Solve can only solve equations which are "essentially algebraic", which means basically all for which they are general non-numerical methods. Your other attempt using SolveAlways is just a case of complete misunderstanding of what this function does. SolveAlways is for "identities". For example: In[12]:= SolveAlways[d + x == d, d] means find x such that for all d, d + x == x, so of course the answer is Out[12]= {{x -> 0}} Your equation SolveAlways[c*(-(a^(1 + d)/(1 + d)) + b^(1 + d)/(1 + d)) == y,d] is saying: find c,a, b and y such that for all d the above relation holds. In fact the relation cannot hold for all d whatever the values of the variables, but in any case this clearly has nothing to do with what you were trying to do. In fact your equation can't be "solved" if by solving you mean expressing a "general solution" in terms of some known functions of the parameters. It is indeed, as you wrote, "mathematically impossible". Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ On Tuesday, July 9, 2002, at 07:51 PM, Björn wrote: > Hello! > > I can't make Mathematica solve an expression for a variable which is > inside an integral. Integrals are of the form: > Integrate[f, {x, xmin, xmax}] > > And my expression is of the kind: > Solve[Integrate[(c x^d), {x, a, b}] == y, d] > > Now, Mathematica can solve for a, b and c. But it cannot solve for d. > Why? > > It gives me the message: > "The equations appear to involve the variables to be solved for in an > essentially non-algebraic way." > > If I try SolveAlways[Integrate[c x^d, {x, a, b}] == y, d], > I get the message: > "The expression (a^(1 + d)) involves unknowns in more than one > argument, so inverse functions cannot be used." > > (It isn't mathematically impossible, right?) > > Most thankful for any help! > > >