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Help me with the trapezium rule please

rock.freak667
Homework Helper
6,230
31
[SOLVED] Help me with the trapezium rule please

1. Homework Statement
[tex]\int _{0} ^{1} e^{-x} dx[/tex]
By using two trapezia of unequal width, with one width,h, and the other (1-h) show that
[tex]T\approx
\frac{1}{2}(e^{-1}+h(1-e^{-1})+e^{-h}[/tex]
2. Homework Equations



3. The Attempt at a Solution

So the sum is given by

[tex]\frac{1}{2}(e^h+1)h + \frac{1}{2}(e^{1-h}+e^h)(1-h)[/tex]

[tex]= \frac{1}{2}(h+e^{1-h}+e^h-he^{1-h})[/tex]

and here is where I can't show it.
 
Last edited:

Answers and Replies

dynamicsolo
Homework Helper
1,648
4
There may be a problem because this line should be

[tex]\frac{1}{2}(e^{-h}+1)h + \frac{1}{2}(e^{-h}+e^{-1})(1-h)[/tex]

Draw a diagram of the exponential curve e^(-x), mark the points on the curve at x = h and x = 1, connect the dots from (0,1) to (h, e^(-h)) and from there to (1, e^(-1)), draw the trapezoids, and find their areas. (What the problem is calling the "widths" are the bases of the trapezoids along the x-axis.)
 
Last edited:
rock.freak667
Homework Helper
6,230
31
ahhhh...dumb me... I drew the diagram correctly but instead of from 0 to 1, I drew from 0 to -1....and I used the wrong x-coordinate...I got it now thanks!
 

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