# Integration of nonnegative function

Can someone explain the results of

Plot[
((E^(-.6 *x))^(-1 + 38) (1 - E^(-.6*x))^(-1 + 160) *.6)/Beta[-1 + 38., 160.],
{x, 1/.6, 4.5}]


and

1/Beta[-1 + 38., 160.]
Integrate[0.6*(E^(-0.6*x))^(-1 + 38)*(1 - E^(-0.6*x))^(-1 + 160), {x, 2, 4.}]


?

• I am getting very large values for functions with reasonable plot Commented Jan 8, 2018 at 7:10
• Try N[1/Beta[-1 + 38, 160]* Integrate[(E^(-6/10 *x))^(-1 + 38) (1 - E^(-6/10*x))^(-1 + 160) *6/ 10, {x, 2, 4}], 30] Commented Jan 8, 2018 at 7:22
• Commented Jan 8, 2018 at 7:28

This is a problem of precision with large numbers.

nint = 1/Beta[-1 + 38., 160.]*
NIntegrate[(E^(-.6 *x))^(-1 + 38) (1 - E^(-.6*x))^(-1 +
160) *.6, {x, 2, 4}]

(*    0.999858    *)

int = 1/Beta[-1 + 38, 160]* Integrate[
Rationalize[(E^(-.6 *x))^(-1 + 38) (1 - E^(-.6*x))^(-1 + 160) *.6,
0], {x, 2, 4}]

(*  A very large output ...   *)

N[int]

(*    -1.35051*10^66    *)

Block[{\$MaxExtraPrecision = 500}, N[int, 10]]

(*    0.9998583622    *)