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9.33. Evaluate (a) (In x)4 dz, (b) (x In z)3 dz, (c) S Vin (1/2) dz.

9.33. Evaluate (a) (In x)4 dz, (b) (x In z)3 dz, (c) S Vin (1/2) dz.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(6) J, * Supplementary Problems GAMMA FUNCTION r(7) 2 Г(4) г(3)" Г(8) г(3/2) Г(9/2) 9.28. Evaluate (a) (b) (с) г(1/2) г(3/2) г(5/2). 00 9.29. Evaluate (а) x4 e-* dx, x8 e-3x dx, (c) x2 e- 2x dx. dx, (b) Vze-VE dz, (e) f" y3 e-2v° dy. 9.30. Find (a) e e-st 9.31. Show that dt = 8 > 0. VE n-1 9.32. Prove that r(n) In dx, n > 0. 231 / 417 (b) S" S Vin (1/x) dx. 9.33. Evaluate (a) (In x)4 dx, (x In x)3 dx, (c) 9.34. Evaluate (а) г(-7/2), (6) г(-1/3). 9.35. Prove that lim r(x) : = 00 where m = 0, 1, 2, 3, ... *- -m (-1)m 2m VT 1• 3• 5... (2m – 1) 9.36. Prove that if m is a positive integer, r(-m + })
Transcribed Image Text:(6) J, * Supplementary Problems GAMMA FUNCTION r(7) 2 Г(4) г(3)" Г(8) г(3/2) Г(9/2) 9.28. Evaluate (a) (b) (с) г(1/2) г(3/2) г(5/2). 00 9.29. Evaluate (а) x4 e-* dx, x8 e-3x dx, (c) x2 e- 2x dx. dx, (b) Vze-VE dz, (e) f" y3 e-2v° dy. 9.30. Find (a) e e-st 9.31. Show that dt = 8 > 0. VE n-1 9.32. Prove that r(n) In dx, n > 0. 231 / 417 (b) S" S Vin (1/x) dx. 9.33. Evaluate (a) (In x)4 dx, (x In x)3 dx, (c) 9.34. Evaluate (а) г(-7/2), (6) г(-1/3). 9.35. Prove that lim r(x) : = 00 where m = 0, 1, 2, 3, ... *- -m (-1)m 2m VT 1• 3• 5... (2m – 1) 9.36. Prove that if m is a positive integer, r(-m + })
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