Apply Gauss Quadrature formula to the following equation

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.

Answer 1

[Torsten]

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.

[Quinten]

I don't understand where the sum goes. I don't understand this at all.

[Torsten]

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.