Evaluate the integral $ 3z + 4)cos z dz, C:12+2i = 1 counterclockwise. z² +4 Integrate...
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.
1. Evaluate the complex integral: ∫C [zRe(z) − z¯Im(z)]dz, where C is the line segment joining −1 to i. (z¯ = z bar) 2. Evaluate the complex integral: ∫ C [iz^2 − z − 3i]dz, where C is the quarter circle with centre the origin which joins −1 to i.
(c) Evaluate the following contour integral: dz tan(z)- 1- iv7
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
Question 1) Find I = z +2 3z - 2 + 3i 22 + (2i - 2)2 - 4i ] dz, C:\z| = 3, CW a. 4πί b. 8πί C. 2πί d. -2π(3 +i) e. 0.0 f. ο g. -4πί h. 6π
Problem 18. 7/2 (1 point) Evaluate the iterated integral AIT cos(x+y+z) dz dx dy. Answer:
(5) Use Cauchy Integral Formula to calculateh(2+(i+1), ee is whose vertices are 0, 4, 2- 2i, and -2i. oriented counterclockwise. Assume a suitable branch of (z +4i) c (2+ I)2 + i dz where C is the paralle 5)
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
Fall (25) 2. Find the limit lim 3z + 12i 27-4i 22 +16 (25) 3. Evaluate the integral positive orientation. cos(12) 4z2 + 8z - 5 dz where C is the circle C: 12+3+ i = 2
Integrate counterclockwise or as indicated. Show the details. cosh dz, C the boundary of the 2-Ti square with vertices +2, 2, ±4i.