Improper (difficult) integrals at SwissMicros Calculator Forum

[peacecalc]

Hello,

@Ajaja, yes the area integral is tricky, because the adaptive quadratur methods fails in the Intervall
from lets say x in 0.5 to 1. And the integral for the arc length will be for such methods good possible fom x in -1 to 0, but for x > 0 the quadratur algorithmus runs into trouble.

@Irdhat in principle it is a good idea to integrate such monsters in smaller areas. But I didn't understand , why you choose the greatest intervall from 10-6 to 1. In my view, je nearer you come to 1 you have to make smaller intervalls, for example:
I -1 to 0
II 0 to 0.5
III 0.5 to 0.7
IV 0.7 to 0.8
VI 0.8 to 0.85
VII 0.85 to 0.88
...
and so on, that can be managed with a program. For the arc length im not shure wether 34 is a correct estimation, because the function is oszillating with a very high frequency (which raises!) between (e^x)*(e^{-1}) and (e^x)*(e^{1}) for example x =0.8 you get a difference value 5.231. For x = 0.8 you get a very great gradient (near vertical plus or minus), so the arc length has to be very long, I assume. But I give hp prime a chance to manage it (with the method above).