Question

5(a)(b) are asking what the Cauchy-Goursat Theorem and the general Cauchy Integral Theorem talks about. Please use these two theorems to solve the problem.

(6) Let C denote the closed contour (3 – sint)et, 0 <t < 2n. Use 5(a)(b) above to aid in computing the following contour integrals. (a) So z?sin(2)dz (b) Jc E-P-5)² dz 24-iz

Answer 1

Solulion and an a Simple closed inside oraly9c f be 5 a) Let in Contooe fy fla) - 0. the cloced POSitively orfented contour be Let b) in the intergeoo o8 . Point be 2o and and On r, then aralyic within is Ck) (20) So fla) (2-20) Ktl य। 6), S2 sin (a) da fla)= 2 Sin (a) Let, ftz) be analytfc însde and adosed (3 - Sfnt )et deg fon COuchy - Gowasht theobem SP2)daoo So, by b) 24_12 Let fla) (2-5)- f'l2) z (2-5)423-1)-1-1D UZ-6) (2-5)4 8-5) (-4i -1) - (1+1) 2ci-5) (9-5)4 ct

5+asi -4 L1-53 Itasi (f-5)3 integal foonula cuochy's 24-92 எட் ஓ't) ெ (2-1) (2-5) ஜாf. (+2) Či-5)3 ப