:00000,?>: as result of interval

[cyrille de brébisson]

Hello,

I did some digging there...

The answer:
1/3*(Gamma (1/3, -216)-Gamma (1/3))-1/3*(Gamma ( 1/3,0)-Gamma(1/3)) 5,96393809188E91

Means that the CAS tried to solve the input (int(e^x^3, x, 0, 6)) in 2 different ways.
One is symbolic (returned the expression) and the second is numerical (returned the number).

It then tried to verify that they matched...

However, the calculation of Gamma (1/3, -216) returned as undefined (the reason is that the numbers are so large (10^91) that the numerical algo used to calculate them do not converge. SO, instead of returning a bad approximate value (which the 5,9e91 number is), it returned an error.

If you look at the function (e^x^3) between 0 and 6, you will see that its value vary enormously. As a result, all the first part of the integration (if you think of it as a summation of area) is completely lost in the final result.
Yes, Prime (and most other calculators) will give you a number as a result, but these number are in lots of way meaningless... This is what the CAS is trying to tell you (in a roundabout way).


Now, the fact that in home you get that wiered :00000,.>: is caused by the fact that the home version of integral was not designed to handle such special cases.

Cyrille