Assume that x, y R and z = x+ iy C and answer the followings....

  

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Assume that x, y €R and z = x+ iy € C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R co, C € (-R, +R) ) x? dx. Jx=-00x++1 a- Reje) x2 b- Jr=- (x2+1)² Figure 1 cos(2x) dx c- Jx=-0 (x2+1)* d- o sin(2x) x=-00 (x2+1)² xsin(x) x=-0 (x2+1)(x2+4) e- eizz (Hint: In section c, firstly calculate S dz for a given z2+4 countour.Then take the real part of result by using euler's formula.You can use same strategy for section d and e by considering imaginary part of result.) Assume that x, y €R and z = x+ iy € C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R co, C € (-R, +R) ) x? dx. Jx=-00x++1 a- Reje) x2 b- Jr=- (x2+1)² Figure 1 cos(2x) dx c- Jx=-0 (x2+1)* d- o sin(2x) x=-00 (x2+1)² xsin(x) x=-0 (x2+1)(x2+4) e- eizz (Hint: In section c, firstly calculate S dz for a given z2+4 countour.Then take the real part of result by using euler's formula.You can use same strategy for section d and e by considering imaginary part of result.)