Exercises

1. Use Maple to compute the following definite and indefinite integrals.
   1. 

   2. , where n is a positive constant.

   3. 

   4. 

   For Exercises 2-5, consider the function: on

2. Approximate the area under the curve for n = 10, 20, 50, using trapezoidal and Simpson's rules.

3. 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 Maple command

   h:= diff(g(x), x$4);

   defines h to be the 4 derivative of g.

4. 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?

5. 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?