Assume that x,y € R and z=x+iy € C. Calculate the part a) using the given countour and assuming that ?→∞. For part b), use variable transformation of z=e3ix. Calculate the part a) using the given countour and assuming that R → 0. For part b),use variable transformation of z = e3ix.(Hint: After variable transformation be careful about how many times we turn around the unit circle.)x3CRа-x8+1C2-2T1dxcos(Зx)+20,45°

(a) We have to solve integral ∫0∞x3x8+1dx in the given contour. Substitute u=x4 ⇒dx=14x3du Hence,…

Calculate the part a) using the given countour and assuming that R → co. For part b), use variable transformation of z = e3ix. (Hint: After variable transformation be careful about how many times we turn around the unit circle.) a- So 00 x3 CR C2 1 b- Jo dx cos(Зx)+2 45°

Calculate the part a) using the given countour and assuming that R → co. For part b), use variable transformation of z = e3ix. (Hint: After variable transformation be careful about how many times we turn around the unit circle.) a- So 00 x3 CR C2 1 b- Jo dx cos(Зx)+2 45°

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 68E

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Question

Assume that x,y € R and z=x+iy € C. Calculate the part a) using the given countour and assuming that ?→∞. For part b), use variable transformation of z=e^3ix.

Calculate the part a) using the given countour and assuming that R → 0. For part b),
use variable transformation of z = e3ix.
(Hint: After variable transformation be careful about how many times we turn around the unit circle.)
x3
CR
а-
x8+1
C2
-2T
1
dx
cos(Зx)+2
0,
45°

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