The Gamma Function and Factorial Function: In this problem you will explore where x is a

Chapter 9, Problem 25

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The Gamma Function and Factorial Function: In this problem you will explore where x is a constant with respect to the integration. Figure 9-10m shows the integrand for x = 1, x = 2, and x = 3. Figure 9-10m a. Find f(1), f(2), and f(3) by evaluating the improper integral. Along the way you will have to show, for instance, that b. From the pattern you see in the answers to part a, make a conjecture about what f(4), f(5), and f(6) are equal to. c. Integrate by parts once and thus show that f(x) = x f(x 1) Use the answer to confirm your conjecture in part b. d. The result of the work in parts a-c forms a basis for the definition of the factorial