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

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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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
Transcribed Image Text: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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how are you getting pi. should it be pi/4 or is it because you are flipping 1/2 to 2/1. I am still confuse 

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