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

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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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