How can you solve for part b. I am very confuse 111. Gamma function The gamma function is defined by I (p) =integer.f(x)=xa. Use the reduction formulaas48=0Г(Р) =to show that I (p+1) = p! (p factorial).b. Use the substitution x = u² and the fact that:SoxX00So xp-¹e* dx → [(p+¹) = P&-X↑u:P-1 -Xe↑dx∞[* pf*:0-b[lim -- XS.:£*]Suv' = uv- Svu00P -X-X- x-x^ |*" - S^«et pati deP-1:-edxpxM = XP_X= [x²-ë² 10 ] + p Soºč“. ‚x“ d«Pol:dx·(0)。)?-.μ' = pxPP-1-X· [o-o] - Sic². M. dedxpXSoc. xf² dxxPex dx = p xP-le-x dx for p = 1, 2, 3, ...8foº eS∞v=-èx': ¿¨**x²-¹e-* dx, for p not equal to zero or a negative√e-u² du =to show that IT ( ²2 ) = √TT.Suv' = uv-SveHow to pick .....IST LLодnverseA lgebraic (+,-, *, *, `√, x^)I rigE xponential

Answered: Image /qna-images/answer/7436faef-6d59-47d2-91dd-23da6bae9d8d.jpg

Answered: b. Use the substitution x = u² and the…

Math

Calculus

b. Use the substitution x = u² and the fact that S e-u² du VI = ¹(²-) = √². to show that I

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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Question

How can you solve for part b. I am very confuse

111. Gamma function The gamma function is defined by I (p) =
integer.
f(x)=x
a. Use the reduction formula
as48=0
Г(Р) =
to show that I (p+1) = p! (p factorial).
b. Use the substitution x = u² and the fact that
:
Sox
X
00
So xp-¹e* dx → [(p+¹) = P&
-X
↑
u
:
P-1 -X
e
↑
dx
∞
[* pf*:
0
-b
[lim -- XS.
:
£*]
Suv' = uv- Svu
00
P -X
-X
- x-x^ |*" - S^«et pati de
P-1
:
-e
dx
px
M = X
P
_X
= [x²-ë² 10 ] + p Soºč“. ‚x“ d«
Pol
:
dx
·(0)
。)?-.
μ' = px
P
P-1
-X
· [o-o] - Sic². M. de
dx
p
X
Soc. xf² dx
xPex dx = p xP-le-x dx for p = 1, 2, 3, ...
8
foº e
S
∞
v=-èx
': ¿¨*
*x²-¹e-* dx, for p not equal to zero or a negative
√
e-u² du =
to show that I
T ( ²2 ) = √TT.
Suv' = uv-Sve
How to pick .....
IST L
L
од
nverse
A lgebraic (+,-, *, *, `√, x^)
I rig
E xponential

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