Use Maple to compute the following definite and indefinite integrals.
, where n is a positive constant.
For Exercises 2-5, consider the function:
Approximate the area under the curve for n = 10, 20, 50, using
trapezoidal and Simpson's rules.
In estimating error, the value M or K is often approximated
by a number N that is an upper bound of M or K. Find upper
bounds on these quantities for the function . Note that the
h:= diff(g(x), x$4);
defines h to be the 4 derivative of g.
If n = 20 and the function is , what accuracy is
guaranteed by the Simpson's error bound formula? By the Trapezoidal
error bound formula? If values from the int command are assumed to be
correct, what accuracy was in fact achieved in each case?
What value of n is reasonable to use if 6 place accuracy is
desired? (i.e. ). Compare the values
of n for each method, including the midpoint rule (See Lab 1,
exercise 3). What conclusion could you draw about the relative
accuracy of the three approximation methods?