(a) option is correct
con #3 (15 pes) Evaluate (05 (22) dz, where C: 12 F 1 2 (m)_271, (b)...
Evaluate Sc(1/22)dz, where C is the line from 1 to 1 + 5i followed by the line from 1+5i to -1 + 5i followed by the line from -1 + 5i to -1. (a) 0 (b) 2 (e) -2 (d) i (e) None of the above. Which of the following integrals is not equal to zero ? a) Sal=10 ze dz b) |--2--(2 – 2)e+/-dz Jul 2 d) cosa 282dz 4) J- 2 e) Si=1 (2–1jadz Which of the numbers...
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.
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...
Q5) Evaluate $c f(z) dz where C is the unit circle Iz| = 1 and f(2) is defined as follows a) f(z) = z2+z2+z_ b) f(x) = tan z c) f() = cosha
Evaluate the integral $ 3z + 4)cos z dz, C:12+2i = 1 counterclockwise. z² +4 Integrate $c +436 yosz dz, C:/z+3–2i = 3 counterclockwise. (z +4)
7. Evaluate the following integral. b) SO3(2-1)05 dz c) f (xl dx (15 marks) 8. A shaded region S is bounded by the curve y = the x-axis, the vertical lines x = 1 and x = V2. The x(4-2)1/4 region is rotated through 21 radians about x-axis to form a solid of revolution. Compute the exact volume of the solid of revolution formed. (10 marks) 9. Between the two towers of a suspension bridge that are 2 kilometres apart,...
please calculate directly, my answer is (3/2)pi+32/3 is that correct? (15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the quarter circle +y 1,x 2 0,y 0, from (0,-1) to (1,0) followed by the arc C2 of the quarter ellipse 4z2y2 - 4, 2 0, y 20, from (1,0) to (0, 2) (15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the...
1 5. Let A = dz, (2 – 1)2(2 + 2i)3 where I is the circle [2] = 3 traversed once counterclockwise. The following is an outline of the proof that A = 0, justify each statement. Jo Tz – 1)*(x + 2133 (a) For R > 3 show that A = A(R) where A(R) Som 1 (z – 1)2(x + 2i)3 dz, and I'R is the circle (2|| = R traversed once counterclockwise. 21R (b) For R > 3...
1 10) (20 pts) Evaluate $. 22 +23+3 dz, C is the e ellipse * + y2 = 1
2. Evaluate the contour integrals, explaining your answers. Give your answers in the form a+bi, where a and b are real a) So 22 dz, where C is any contour which begins at 2 = 1 and ends at z = 2i b) S dz where C is any contour which begins at z=1 and ends at z = 2i, and does not cross the negative real axis or go through 2 = 0.