Apply Gauss Quadrature formula to the following equation

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Quinten
Quinten 2016-11-17
评论： Torsten 2016-11-18
given the equation
d = gm/c integral [0,10] [1 - exp(-(c/m)t)]dt
g = 9.8
c = 12.5
m = 68.1
employ two- through six-point gauss-legendre formulas to solve.
I have no idea what i'm doing and would love help.

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回答（1 个）

Torsten
Torsten 2016-11-17
编辑：Torsten 2016-11-17
You are supposed to evaluate
5*sum_{i=1}^{i=n} w_i*f(5*x_i+5)
with
f(x) = g*m/c*(1 - exp(-(c/m)x))
for n = 2,3,4,5,6 and the corresponding x_i and w_i specified under
https://pomax.github.io/bezierinfo/legendre-gauss.html
(or in your textbook).
Best wishes
Torsten.
  2 个评论
Quinten
Quinten 2016-11-17
编辑：Quinten 2016-11-17
I don't understand where the sum goes. I don't understand this at all.
Torsten
Torsten 2016-11-18
To approximate the integral, the function f is evaluated at n intermediate x-values in the interval [a,b]. The n function values so obtained are then weighted by the w_i and summed - that's all.
I think it's best if you first try to understand the procedure from a textbook before you start programming.
Best wishes
Torsten.

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