Quiz: calculating a definite integral

[Thomas Klemm]

(12-31-2013 04:24 AM)Namir Wrote:  I do believe the program should be:

Code:

01 LBL 0
02 ENTER
03 CHS
04 yx
05 RTN

For the built-in integral to work!

The HP-15C conveniently fills the stack with \(x\) when calling your function.

Quote:I would use an open Newton-Cote numerical integration method since this class of methods do not evaluate the integral at the end points, just in case my machine barks at evaluating 1/0^0.

Good point. The function is continuous even at 0: \(\lim_{x\to0}x^{-x}=1\)

But the first derivative is singular at 0: \(\lim_{x\to0}\frac{\partial x^{-x}}{\partial x}=\infty\)
HP's modified Romberg method avoids the end-points of the interval as well.