The measured values of a force () as a function of the displacement are given in Table 6.9. The object of this exercise is to calculate the work . (a) Use the trapezoidal rule to find the value of ()...

The measured values of a force
() as a function of the displacement
are given in Table 6.9. The object of this exercise is to calculate the work
.

(a) Use the trapezoidal rule to find the value of
() at

= 2, 4, 6, 8. You can assume that
(0) = 0.

(b) Use the composite midpoint rule to calculate
(8).

(c) Use the composite Simpson rule to calculate
(8).

(d) Use Romberg integration with the composite trapezoidal rule to calculate
(8).