practice exam c

U t0 agreed step 2 u0 accordingly us1 u du

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: −(u+λ) t dt u > 0, 1 . u+λ = t=0 Agreed. Step 2. +∞ u=0 Accordingly, us−1 u+λ +∞ du = u=0 +∞ = t=0 us−1 · +∞ t=0 us−1 · e−u t du e−λ t dt Γ ts 5 e−(u+λ) t dt du +∞ u=0 Line #: 23590. Name : ID # : ([III] (1) continued) +∞ · =Γ · e−λ t dt t t=0 Γ λ1−s =Γ · λs−1 . ·Γ (functional identity) π sin πs In short, +∞ u=0 us−1 u+λ π du = sin 6 πs · λs−1 . Line #: 23590. Name : ID # : ([III] continued) (2) Rewrite the result of (1) as +∞ u=0 1 u+λ sin · us−1 · πs Integrate the both sides as in indefinite integrals +∞ u=0 1 u+λ · us−1 · u=0 1 u+λ ln u ·...
View Full Document

This note was uploaded on 01/12/2014 for the course MATH 116 taught by Professor Scholle,minho during the Fall '08 term at Kansas.

Ask a homework question - tutors are online