Exercise: work from tabulated data

With step 1.52 and data F=[0,40.04,57.83,62.28,46.71,53.38,22.24], alpha=[0.5,1.4,0.75,0.9,1.3,1.48,1.5], compute W=∫F(x)cos(alpha(x))dx.

1. First build the tabulated integrand by multiplying F by cos(alpha):

   $$g_i=F_i\cos(\alpha_i)$$

2. Applying trapezoid and Simpson to the measured data gives:

   $$T=161.0507484870318,\qquad S=158.3980289247424$$

3. For midpoint, interpret the data as central heights and use auxiliary nodes of step 1.52/2:

   $$M=162.24638$$