please only calculate a) and b). ignore the hint 1-) Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reelintegrals for a given countour in figure 1.(Consider R → 0, C € (-R,+R) )Imfz}x2a- S-o dx∞ x4+1Re(z}-RRb- Se-o (x²+1)?Figure 1X=-∞cos(2x)dxC-:- 00sin(2x)x=-∞ (x²+1)²xsin(x)dx-Sr=- x²+1)(x²+4)(Hint: In section c , firstly calculate Jcz2+4eizdz for a givencountour.Then take the real part of result by using euler'sformula.You can use same strategy for section d and e byconsidering imaginary part of result.)

Given: (a) ∫-∞∞ x2x4+1 dx (b) ∫-∞∞ x2(x2+1)2 dx We have to calculate the (a) and (b)

1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R → 00, C e (-R,+R) ) Im{2} x2 a- S x=-∞ x4+1 ax Re(z} R b- Sr-o (x2+1)? x2 Figure 1 x=-∞ (x²+1)² cos(2x) dx x=-∞ (x²+1)² C- sin(2x) d- x=-∞ (x2+1)² x xsin(x) e- е- x=-∞ (x²+1)(x²+4)

1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R → 00, C e (-R,+R) ) Im{2} x2 a- S x=-∞ x4+1 ax Re(z} R b- Sr-o (x2+1)? x2 Figure 1 x=-∞ (x²+1)² cos(2x) dx x=-∞ (x²+1)² C- sin(2x) d- x=-∞ (x2+1)² x xsin(x) e- е- x=-∞ (x²+1)(x²+4)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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