Question

Exercise 10.12. i) (A contour integral) Let TR -R, RSR, where R E (1, 0o) half-plane with centre 0 that goes and SR is the semicircular arc in the upper from R to-R. Use a clear sketch of「R and the calculus of residues to evaluate the integral 「R 1+24 , and then decide which of the following five statements is true: (A) Rel < -3 (B) ReI e [-3,-1); (C) ReI [-1,1) (D) ReI E [1, 3); (ii) (An integral over the positive reals) Use the result of (i) to help find the integral and then decide which of the following five statements is true: 25 (B) JE 1,2); (C) J E [2,3); (D) JE 3,4); (E) J 4

Answer 1

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4- Ces 4 7 4 LTV Les 4- 4 Scanned with CamScanner

4- 4 UE Canaidu CS Scanned with CamScanner

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嗄 ve V& VA 는 -40-4 Scanned with CamScanner

4 -4-+40 지 4- V3. 자 0 C Scanned with CamScanner

dz dz 4 4 R. 지 i+z4 LO tz4 4- 7 Scanned with CamScanner

즈! 2. 4 0 4 Scanned with CamScanner