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Question: An integral needs to be calculated.

Question:An integral needs to be calculated.

Alfred_F 450 Maple
integral closed-form
1 hour ago
0

In the attached file, I want to calculate the integral Q1. Numerically, this is easy to do in Maple. For theoretical reasons, the exact result pi/e is known. However, a contradiction arises between command lines (4) and (5). Command (6) is also unsuccessful, as its exact result is unknown. What am I doing wrong?test.mw
 

restart

Q1 := int(sin(Pi*x)/(x^x*(1-x)^(1-x)), x = 0 .. 1)

int(sin(Pi*x)/(x^x*(1-x)^(1-x)), x = 0 .. 1)

 (1)

evalf[100](Q1)

1.155727349790921717910093183312696299120851023164415820499706535327288631840916939440188434235673559

 (2)
> 

evalf[100](Pi/exp(1))

1.155727349790921717910093183312696299120851023164415820499706535327288631840916939440188434235673559

 (3)
> 

is(Q1 = Pi/exp(1))

false

 (4)
> 

identify(evalf[100](Q1))

Pi*exp(-1)

 (5)

identify(.2340257795502385151002175791580229871350403567739388325733228478980460706709848394726222465477567339)

.2340257795502385151002175791580229871350403567739388325733228478980460706709848394726222465477567339

 (6)

NULL


 

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