Elaborating some earlier programs

  1. New version of the table of factorials program: write to a file instead of the screen.
  2. New version of the program to compute the integral of the function f(x) = fourth root of 1 - x^2 on the interval [0,1]: it should declare f as a C function.
  3. The integral of e^{x^2/2}
  4. The series 1 + 1/2^3 + 1/3^3 + 1/4^3 + ...

Problem 1.

Rewrite your factorial program so that it writes its output to a file using fopen and fprintf.

Problem 2

Rewrite your program to compute the integral of the fourth root of 1 - x^2 on the interval [0,1] so that it uses a function declaration.

Problem 3

Modify the previous program to compute the integral of e^{-x^2/2} on the interval [-1,1]. Aim for two decimals of accuracy and discuss the precision actually obtained. Make a sketch of the geometric figure whose area the integral represents.

Problem 4

Write a program which computes the sum
  f(1) + f(2) + \cdots + f(n)
where f is an arbitrary function delared as a C function and where the user specifies n. Use this program to compute an approximation to the sum
   beta = 1 + 1/2^3 + 1/3^3 + 1/4^3 + ...
accurate to two decimal places. What value of n need to achieve this accuracy? Justify your answer.
Back to syllabus
Back to Department of Mathematics, University of Utah
Last modified: Feb 22, 1995
Copyright © 1995 Department of Mathematics, University of Utah