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[SOLVED] Help me with the trapezium rule please
[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]
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.
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]
Homework Equations
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.
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