numerical computation challenge

[MechEng83]

Originally Posted by Michael Hill

I took the initial y=... function and rotated it by pi/4 (45 degrees) using the transformation matrix:

y'     [cos(pi/2) sin(pi/2)] [y]
   =
x'     [cos(pi/2) -sin(pi/2)] [x]

That allows me to essentially take the integral above the new y' and simply multiply it by 2.

Rather than going through the trouble of transforming it, I just subtracted the integral of y=x, as that's the symmetry line.

I got 0.536595 for the area -- found the second intercept at .95012, then just took the integral from 0 to .95012 of [10*ln(x)/exp(x)-x] and multiplied by 2.

[Ether]

Nice job guys. The key was using the y=x symmetry line.

In the attached graph, the red and green lines are the two curves. The cyan line y=x is the axis of symmetry. If you subtract the cyan line from the red curve, you get the black curve.

I used Maxima to find the X-axis intercept of the black curve, and then numerically integrate the black curve from zero to that value and double it.

[Michael Hill]

Of course I go the complicated route. This transcends to my ideas for robots as well. I need to learn to be more elegant. :-P