Question

please help with all parts of the question, thanks in advance!

#5: Compute the following integrals for each of the cases R = 1, R = 5, R = 20 using as needed the facts in part # 4 a,b,c. Jx=R*** dz, Jx1=R (3-2)2-4) dz, S(x1=R 72-72 dz, Jx1=R (2–3)212–70)2 dz

Answer 1

We know the Cauchy's integral formulare if (8) is anasytic inside and on a simple closed curre c and air any point inside ce them NEN. Now R21 873 2d22 273 12121 244 24+42261) [trans] 12121 2173 1812+21)(2-22) Now CEBUJE 243= A(Z-24 ) + 6(E+22') putting zeer and 22r2, we get (21) f 32 Andit Bo42 27-4435 482 27 4Bir alan 4Blaen as 4Bel ar be u

Also, (22) 73 2 A (-21-22) & B. o >> -443 = A(-42) 7+12+A4i >> As the BY AP Here Hence | 273 (422) (3:21) 2 %)dą ) 1) ہے ( z!= 1 2-22 2121 z Oto zo l'as Zeu2nd and L agu Lires Again outside for Ras of 12/27 . 7 243 1212, 2+21) (221) tiheldz T (eu) dz R125 Z4270 t J 2-2,! 12/25 2012" X A 6 14) + 2x2 X 1X2%

Similarly for R220, from the da + (%) do 12/220 274 12/220 2-22 12/220 2 212X-144) et 262°N 1X zo 2005 Edice-ve let z Á LE-11) - Anitta te-2) (2-42) 1212R 27 za A(Z-42') at B (2-2) putting zo 42 and 282, we get | 4 = Aoi 0 (+2) & Bee e 42! Also, 20 A (2-42") of Bio * * AF E *) = lyder det (42 44-2 Z2

for Ral 2-2)(2-42) + 4E-2) da 7-2 2-42 1212) soro[ree and zahlres - outside of 12/21 7 20 for R25 file noastre) - 640)ale. I love you love 12/25 2420 12/25 - LEXO Y + 26*21* en team - inside 12/24 452 Lr67 81L 4222 Similarly for R220, T erbove) -( (lzemelez a 45 20.) da 112122 202 Bo er42 12220 sem To [sanne loke 87 =2 and zou ulics insale of 121220]

Ternery) for R21 Ral Since of lies outsick 1212, (2-7) of 18121 verstehe 20 [shou en of het ontrole of 2o Sime zoq tires outside 12/25 121=20 2t 2 242x 675 1204 2 2 кухът e 33 614a , Hence the result.

(23) (242) for Rol per Eligna (1/640) 1/2-3) 1212 € 3) (Zrtigh I (Zrz) I 18421 + J (2-492. 12124 2010 as e=% and 2077 a Llires outside of 18120 Bles 3) Zoffrigh bin't _lzog's 12/25 ( 231754 I T2-72) 18125 - 2009 Listo] to

ਇਸ ਦੇ ਲਈ ੭) (ਜਨs | ... 2 ਨੇ ! for R=20, ( ਲ 7-75 Thਨ ਇਹ ) 7 ਇlze ਖ | z " + • Bਦੇ ਵਚਮੀ . 2.6 " 2 2rx2) · L ਦੇ 75 3 S:* (-2) · ਤ ਇਹ tena the result,