Chapter 6: Techniques of Integration
Section 6.7: Numeric Methods
Use the Trapezoid rule to approximate the area under the curve determined by the following data points.
Table 6.7.7(a) Data points determining a curve
Figure 6.7.7(a) shows the eleven data points and the piecewise linear curve connecting them.
The Trapezoid rule, with n=10 and h=1/5 gives the area A as
use plots in
for k from 0 to 10 do
f[k] := evalf(eval(q,x=-1+k/5),4);
Figure 6.7.7(a) Piecewise linear curve
Of course, the most tedious part of the calculation is entering the data!
Enter the data
Form a list of the eleven function values in Table 6.7.7(a).
Context Panel: Assign to a Name≻f
13,7.523,4.679,3.528,3.436,4,4.971,6.175,7.440,8.516,9→assign to a namef
Apply the Trapezoid rule
Because lists are enumerated from 1, the eleven data points must be referenced as fk,k=1,…,11.
1/52f1+f11+2∑k=210fk = 12.25360000
The use of a list for the function values is a simplification that is counterbalanced by the need to shift the indices of the data points upward by 1.
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