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

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

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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Please help number 33. Using gamma functions. Please

(6) J, * Supplementary Problems GAMMA FUNCTION r(7) 2 Г(4) г(3)" Г(3) 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. 'dæ, (b) Vze-V= dz, (e) y3 e-20° 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. 9.33. Evaluate (a) (In x)4 dx, (x In x)³ dx, (c) I Vin (1/2) dzr. 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 V7 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(3) 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. 'dæ, (b) Vze-V= dz, (e) y3 e-20° 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. 9.33. Evaluate (a) (In x)4 dx, (x In x)³ dx, (c) I Vin (1/2) dzr. 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 V7 1•3• 5..· (2m – 1) 9.36. Prove that if m is a positive integer, r(-m + })
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