**1.** Prove that

if f(`x`) and g(`x`) are functions which are integrable on [`a`,`b`].

**2.** Consider the polynomial h(`x`) = `x`^{2} - `x` + 41. Note that h(1) = 41, h(2) = 43, h(3) = 47, h(4) = 53, and h(5) = 61 are all prime numbers. Is h(`x`) always a prime number if `x` is a positive integer? Why or why not?

**Solution.** h(41) = 41^{2} - 41 + 41 = 41^{2}.

**Bonus.** Is there any (other?) polynomial which always gives you prime numbers?

Assignment #6

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 1998.08.22.