error while using solve function with integral

2016 4 2
1 个回答
更新时间：2016 4 11
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Please suggest the solution for the encoutering problem below:
syms x V; Pr=solve( int(x.^2.* exp(-x-1./(x+V)),x,1,inf )-0.5 ==0,V);

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回答（1 个）

Walter Roberson
Walter Roberson 2016-4-2

0 个投票

That equation has no real-valued solution. Are you expecting a complex-valued solution?

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modem sudhakar
modem sudhakar 2016-4-2
编辑：Walter Roberson 2016-4-2
No walter, I am expecting real value solution. The value of 'C' can be varied in the program below. At what value of 'C', I can obtain real value.
C=0.5; syms x V; Pr=solve( int(x.^2.* exp(-x-1./(x+V)),x,1,inf )-C ==0,V);
How you find that it will result complex-value?. While I am running it is giving the error like below:
syms x V; Pr=solve( int(x.^2.* exp(-x-1./(x+V)),x,1,inf )-0.5 ==0,V);
Warning: Explicit integral could not be found.
Error using mupadengine/feval (line 157)
MuPAD error: Error: The second argument must be of form x or x = a..b. [int]
Error in solve (line 160)
sol = eng.feval('symobj::solvefull',eqns,vars);
Walter Roberson
Walter Roberson 2016-4-2
The lower limit is at V = -1 exactly, where the integral is approximately .9526391033789570 . The upper bound is V approach infinity where the integral is 5/e which is approximately 1.839397205857212
When V < -1 then the integral is infinite.
Walter Roberson
Walter Roberson 2016-4-11
Notice that because the lower limit is about 0.95, it can never be 0, so there are no real-valued solutions.
modem sudhakar
modem sudhakar 2016-4-11
编辑：modem sudhakar 2016-4-11
Dear walter, I plotted the function by varying V as:
for V=0:1:10 plot(V,integral(@(x) x.^2.* exp(-x-1./(x+V)),1,inf )); hold on end
From this I can see that it is giving positive values. So, if I want get value of V for given integral value as:
solve(integral(@(x) x.^2.* exp(-x-1./(x+V)),1,inf ))==1.4,V)
From above 'for' loop the value should come as V=1. But it is giving the error as:
Undefined function or variable 'V'.
Error in @(x)x.^2.*exp(-x-1./(x+V))
Error in integralCalc/iterateScalarValued (line 314) fx = FUN(t);
Error in integralCalc/vadapt (line 133) [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Walter Roberson
Walter Roberson 2016-4-11
You need to make the integral symbolic. Then vpasolve for V

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