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numerical computation challenge
Find the area between these two curves, accurate to 6 decimal places: y=10*ln(x+1)/exp(x+1) x=10*ln(y+1)/exp(y+1) Use whatever computer tools you want. Show your work. |
Re: numerical computation challenge
I think I solved it....
I got 0.536594(7|8) My strategy was to use the fact that it was symmetric about x=y. I took the initial y=... function and rotated it by pi/4 (45 degrees) using the transformation matrix: Code:
[y'] [cos(pi/4) sin(pi/4)] [y]Code:
clear |
Re: numerical computation challenge
Quote:
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. |
Re: numerical computation challenge
2 Attachment(s)
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. |
Re: numerical computation challenge
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
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