Question

Evaluate the following integrals. In each case, take the orientation of C to be counterclockwise. If you use one of the theorems/formulas given in the SUMMARY section above, - state the name of the theorem/formula as given in the SUMMARY section, - identify the function and the variables in the formula as they apply to the integral you are solving. For example, if you use Cauchy's integral formula, state what you take f(z) to be, and what you take z0​ to be. (Part 3a) (2 points) For C= the circle given by ∣z−π∣=π, ∫C​cos(2z)dz (Part 3b) (2 points) For C= the circle given by ∣z−π∣=π, ∫C​(z2−π2)cos(2z)​ (Part 3c) (2 points) For C= the circle given by ∣z−π∣=π ∫C​(z−π)2cos(2z)​

Answer 1

N

F= -2y² ↑ +32²; + xx

Curl = î x=-6zi-j + by k 1-2y2 372 x

ди

2

Pera motarize the surface of pline: x=M

y = v 6-24-3v= 2= 4 j

A

ds=(ru xv) du dv=

du dv

д

2

о

du

→Stoke's theorem: = √({21 +34 + 25x) dud dv

= √((-32 = 2 + by) du dv =

= SS [³ ( + - + -2x) - 2 + bx] du dv